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The Life and Work of M. M. Rao

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Publisheed Writings of M. M. Rao

  1. M. M. Rao Note on a remark of Wald, Amer. Math. Monthly 65 (1958), 277–278.

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  2. M. M. Rao Lower bounds for risk functions in estimation, Proc. Nat’l Acad. of Sciences 45 (1959), 1168–1171.

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  3. M. M. Rao Estimation by periodogram, Trabajos de Estadistica 11 (1960), 123–137.

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  4. M. M. Rao Two probability limit theorems and an application, Indagationes Mathematicae 23 (1961), 551–559.

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  5. M. M. Rao Theory of lower bounds for risk functions in estimation, Mathematische Annalon 143 (1961), 379–398.

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  6. M. M. Rao Consistency and limit distributions of estimators of parameters in explosive stochastic difference equations, Annals of Math. Stat. 32 (1961), 195–218.

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  7. M. M. Rao Some remarks on independence of statistics, Trabajos de Estadistica 12 (1961), 19–26.

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  8. M. M. Rao Remarks on a multivariate gamma distribution, Amer. Math. Monthly 68 (1961), (with P. R. Krishnaiah, 342–346).

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  9. M. M. Rao Theory of order statistics, Mathematische Annalen 147 (1962), 298–312.

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  10. M. M. Rao Nonsymmetric projections in Hilbert Space, Pacific J. Math. 12 (1962), 343–357, (with V. J. Mizel).

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  11. M. M. Rao Characterizing normal law and a nonlinear integral equation, J. Math. Mecli. 12 (1963), 869–880.

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  12. M. M. Rao Inference in stochastic processes-I, Teoria Veroyatnastei i ee Primeneniya 8 (1963), 282–298.

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  13. M. M. Rao Some inference theorems in stochastic processes, Bull. Amer. Math. Sec. 68 (1963), 72–77.

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  14. M. M. Rao Discriminant analysis, Annals of Inst. of Stat. Math. 15 (1963), 11–24.

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  15. M. M. Rao Bayes estimation with convex loss, Annals of Math. Stat. 34 (1963), 839–846, (with M.H. DeGroot).

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  16. M. M. Rao Stochastic give-and-take, J. Math. Anal. & Appl. 7 (1963), 489–498, (with M.H. DeGroot)

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  17. M. M. Rao Averagings and quadratic equations in operators, Carnegie-Mellon Univesity Technical Report # 9 (1963) 27 pages, (with V. J. Mizel)

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  18. M. M. Rao Projections, generalized inverses, and quadratic forms, J. Math. Anal. & Appl. 9 (1964), 1–11, (with J. S. Chipman).

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  19. M. M. Rao Decomposition of vector measures, Proceedings of Nat’l. Acad. of Sciences 51 (1964), 771–774.

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  20. M. M. Rao Decomposition of vector measures, Proceedings of Nat’l. Acad. of Sciences 51 (1964), 771–774, Erratum, 52 (1964), p. 864.

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  21. M. M. Rao Linear functionals on Orlicz spaces, Nieuw Archief voor Wiskunde 312 (1964), 7798.

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  22. M. M. Rao The treatment of linear restrictions in regression analysis, Econometrica 32 (1964), 198–209, (with J.S. Chipman).

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  23. M. M. Rao Conditional expectations and closed projections, Indagationes Mathematicae 27 (1965), 100–112.

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  24. M. M. Rao Smoothness of Orlicz spaces-I and II, Indagationes Mathematicae 27 (1965), 671680, 681–690.

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  25. M. M. Rao Existence and determination of optimal estimators relative to convex loss, Annals of Inst. of Stat. Math 17 (1965), 113–147.

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  26. M. M. Rao Interpolation, ergodicity, and martingales, J. of Math. & Mech. 16 (1965), 543–567.

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  27. M. M. Rao Inference in stochastic processes-II, Zeitschrift fur Wahrscheinlichkeitstheorie 5 (1966), 317–335.

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  28. M. M. Rao Approximations to some statistical tests, Trabajos de Estadistica 17 (1966), 85–100.

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  29. M. M. Rao Multidimensional information inequalities and prediction, Proceedings of Int’l. Sym-posium on Multivariate Anal., Academic Press, (1966) 287–313, (with M.H. DeG-root).

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  30. M. M. Rao Convolutions of vector fields and interpolation, Proceedings of Nat’l. Acad. Sciences 57 (1967), 222–226.

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  31. M. M. Rao Abstract Lebesgue-Radon-Nikodym theorems, Annali di Matematica Pura ed Applicata (4)76 (1967), 107–132.

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  32. M. M. Rao Characterizing Hilbert space by smoothness, Indagationes Mathematicae 29 (1967), 132–135.

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  33. M. M. Rao Notes on pointwise convergence of closed martingales, Indagationes Mathematicae 29 (1967), 170–176.

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  34. M. M. Rao Inference in stochastic processes-III, Zeitschrift fur Wahrscheinlichkeitstheorie 8 (1967), 49–72.

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  35. M. M. Rao Characterization and extension of generalized harmonizable random fields, Proceedings Nat’l. Acad. Sciences 58 (1967), 1213–1219.

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  36. M. M. Rao Local functionals and generalized random fields, Bull. Amer. Math. Soc. 74 (1968), 288–293.

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  37. M. M. Rao Extensions of the Hausdorff-Young theorem, Israel J. of Math. 6 (1968), 133–149.

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  38. M. M. Rao Linear functionals on Orlicz spaces: General theory, Pacific J. Math. 25 (1968), 553585.

  39. M. M. Rao Almost every Orlicz space is isomorphic to a strictly convex Orlicz space, Proceedings Amer. Math. Soc. 19 (1968), 377–379.

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  40. M. M. Rao Predictions nonlineares et martingales d’operateurs, Comptes rendus (Academie des Sciences, Paris), Ser. A, 267 (1968) 122–124.

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  41. M. M. Rao Representation theory of multidimensional generalized random fields, Proceedings 2d Int’l. Sympt. Multivariate Anal., Academic Press (1969), 411–436.

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  42. M. M. Rao Operateurs de moyednes et moyennes conditionnelles, C.R. Acad. Sciences, Paris, Ser. A, 268 (1969), 795–797.

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  43. M. M. Rao Produits tensoriels et espaces de fontioiis, C.R. Acad. Sci., Paris 268 (1969), 15991601.

  44. M. M. Rao Stone-Weierstrass theorems for function spaces, J. Math. Anal. 25 (1969), 362–371.

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  45. M. M. Rao Contractive projections and prediction operators, Bull. Amer. Math. Sec. 75 (1969), 1369–1373.

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  46. M. M. Rao Generalized martingales, Proceedings lst Midwestern Symp. on Ergodic Theory Prob., Lecture Notes in Math., Springer-Verlag, 160 (1970), 241–261.

  47. M. M. Rao Linear operations, tensor products and contractive projections in function spaces, Studia Math. 38, 131–186, Addendum 48 (1970), 307–308.

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  48. M. M. Rao Approximately tame algebras of operators, Bull. Acad. Pol. Sci., Ser. Math. 19 (1971), 43–47.

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  49. M. M. Rao Abstract nonlinear prediction and operator martingales, J. Multivariate Anal. 1 (1971), 129–157, Erratum, 9. p. 646.

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  50. M. M. Rao Local functionals and generalized random fields with independent values, Teor. Verojatnost., Prem. 16 (1971), 466–483.

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  51. M. M. Rao Projective limits of probability spaces, J. Multivariate Anal. 1 (1971), 28–57.

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  52. M. M. Rao Contractive projections and conditional expectations, J. Multivariate Anal. 2 (1972), 262–381, (with N. Dinculeanu).

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  53. M. M. Rao Prediction sequences in smooth Banach spaces, Ann. Inst. Henri Poincare, Ser. B, 8 (1972), 319–332.

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  54. M. M. Rao Notes on characterizing Hilbert space by smoothness and smooth Orlicz spaces, J. Math. Anal. & Appl. 37 (1972), 228–234.

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  55. M. M. Rao Abstract martingales and ergodic theory, Proc. 3rd Symp. on Multivariate Anal., Academic Press (1973), 100–116.

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  56. M. M. Rao Remarks on a Radon-Nikodym theorem for vector measures, Proc. Symp. on Vector & Operator Valued Measures and Appi., Academic Press (1973), 303–31

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  57. M. M. Rao Inference in stochastic processes-IV: Predictors and projections, Sankhya, Ser. A 36 (1974), 63–120.

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  58. M. M. Rao Inference in stochastic processes-V: Admissible means, Sankhya, Ser. A. 37 (1974), 538–549.

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  59. M. M. Rao Extensions of stochastic transformations, Trab. Estadistica 26 (1975), 473–485.

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  60. M. M. Rao Conditional measures and operators, J. Multivariate Anal. 5 (1975), 330–413.

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  61. M. M. Rao Compact operators and tensor products, Bull. Acad. Pol. Sci. Ser. Math. 23 (1975), 1175–1179.

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  62. M. M. Rao Two characterizations of conditional probability, Proc. Amer. Math. Sec. 59 (1976), 75–80.

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  63. M. M. Rao Conjugate series, convergence and martingales, Rev. Roum. Math. Pures et Appl. 22 (1977), 219–254.

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  64. M. M. Rao Inference in stochastic processes-VI: Translates and densities, Proc. 4th Symp. Multivariate Anal., North Holland, (1977), 311–324.

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  65. M. M. Rao Bistochastic operators, Commentationes Mathematicae, Vol. 21 March, (1978), 301313.

  66. M. M. Rao Asymptotic distribution of an estimator of the boundary parameter of an unstable process, Ann. Statistics 6 (1978), 185–190.

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  67. M. M. Rao Convariance analysis of nonstationary time series, Developments in Statistics I (1978), 171–225.

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  68. M. M. Rao Non L1-bounded martingales, Stochastic Control Theory and Stochastic Differential Systems, Lecture Notes in Control and Information Sciences, 16 (1979), 527–538, Springer Verlag.

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  69. M. M. Rao Processus lineaires sur C00(G), C. R. Acad. Sci., Paris, 289 (1979), 139–141.

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  70. M. M. Rao Convolutions of vector fields-I, Math. Zeitschrift, 174 (1980), 63–79.

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  71. M. M. Rao Asymptotic distribution of an estimator of the boundary parameter of an unstable process, Ann. Statistics 6 (1978), 185–190, Correction, Ann. Statistics 8 (1980), 1403.

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  72. M. M. Rao Local Functionals on C00(G) and probability, J. Functional Analysis 39 (1980), 23–41.

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  73. M. M. Rao Local functionals, Proceedings of Oberwolfach Conference on Measure Theory, Lecture Notes in Math. 794, Springer-Verlag (1980), 484–496.

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  74. M. M. Rao Structure and convexity of Orlicz spaces of vector fields, Proceedings of the F.B. Jones Conference on General Topology and Modern Analysis, University of California, Riverside(1981), 457–473.

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  75. M. M. Rao Stochastic processes and cylindrical probabilities, Sankhya, Ser. A (1981), 149–169.

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  76. M. M. Rao Application and extension of Cramer’s Theorem on distributions of ratios, In Contributions to Statistics and Probability, North Holland (1981), 617–633.

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  77. M. M. Rao Harmonizable processes: structure theory, L’Enseignement Mathematique, 28 (1982), 295–351.

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  78. M. M. Rao Domination problem for vector measures and applications to non-stationary processes, Oberwolfach Measure Theory Proceedings, Springer Lecture Notes in Math. 945 (1982), 296–313.

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  79. M. M. Rao Bimeasures and sampling theorems for weakly harmonizable processes, Stochastic Anal. Appl. 1 (1983), 21–55, (with D.K. Chang).

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  80. M. M. Rao Filtering and smoothing of nonstationary processes, Proceedings of the ONR workshop on “Signal Processing”, Marcel-Dekker Publishing (1984), 59–65.

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  81. M. M. Rao The spectral domain of multivariate harmonizable processes, Proc. Nat. Acad. Sci. U.S.A. 81 (1984), 4611–4612.

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  82. M. M. Rao Harmonizable, Cramér, and Karhunen classes of processes, Handbook in Vol. 5 (1985), 279–310.

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  83. M. M. Rao Bimeasures and nonstationary processes, Real and Stochastic Analysis, Wiley & Sons (1986), 7–118, (with D.K. Chang).

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  84. M. M. Rao A commentary on “On equivalence of infinite product measures”, in S. Kakutani’s selected works, Birkhauser Boston Series (1986), 377–379.

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  85. M. M. Rao Probability, Academic Press, Inc., New York, Encyclopedia of Physical Science and Technology, Vol. 11 (1987), pp. 290–310.

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  86. M. M. Rao Special representations of weakly harmonizable processes, Stochastic Anal. (1988), 169–189, (with D.K. Chang).

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  87. M. M. Rao Paradoxes in conditional probability, J. Multivariate Anal., 27, (1988), pp. 434–446.

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  88. M. M. Rao Harmonizable signal extraction, filtering and sampling Springer-Verlag, Topics in Non-Guassian Signal Processing, Vol. II (1989), pp. 98–117.

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  89. M. M. Rao A view of harmonizable processes, North-Holland, New York, in Statistical Data Analysis and Inference (1989), pp. 597–615.

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  90. M. M. Rao Bimeasures and harmonizable processes; (analysis, classification, and representation), Springer-Verlag Lecture Notes in Math., 1379, (1989), pp. 254–298.

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  91. M. M. Rao Sampling and prediction for harmonizable isotropic random fields, J. Col Analysis, Information & System Sciences, Vol 16 (1991), pp. 207–220.

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  92. M. M. Rao L2,2 boundedness, harmonizability and filtering, Stochastic Anal. App., (1992), pp. 323–342.

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  93. M. M. Rao Probability (expanded for 2nd ed.), Encyclopedia of Physical Science and Technology Vol 13 (1992), pp. 491–512.

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  94. M. M. Rao Stochastic integration: a unified approach, C. R. Acad. Sci., Paris, Vol 314 (Series 1), (1992), pp. 629–633.

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  95. M. M. Rao A projective limit theorem for probability spaces and applications, Theor. Prob. and Appl., Vol 38 (1993), (with V. V. Sazonov, in Russian), pp. 345–355.

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  96. M. M. Rao Exact evaluation of conditional expectations in the Kolmogorov model, Indian J. Math., Vol 35 (1993) pp 57–70.

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  97. M. M. Rao An approach to stochastic integration (a generalized and unified treatment) in Multivariate Analysis: Future Directions, Elsivier Science Publishers, The Netherlands (1993), pp. 347–374.

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  98. M. M. Rao Harmonizable processes and inference: unbiased prediction for stochastic flows, J. Statistic. Planning and Inf., Vol 39 (1994), pp. 187–209.

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  99. M. M. Rao Some problems of real and stochastic analysis arising from applications, Stochastic Processes and Functional Analysis, J. A. Goldstein, N. E. Gretsky, J.J. Uhl, editors, Marcel Dekker Inc. (1997), 1–15.

  100. M. M. Rao Packing in Orlicz sequence spaces, (with Z. D. Ren), Studia Math. 126 (1997), no. 3, 235–251.

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  101. M. M. Rao Second order nonlinear stochastic differential equations, Nonlinear Analysis, Vol. 30, no. 5 (1997) 3147–3151.

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  102. M. M. Rao Higher order stochastic differential equations. Real and Stochastic Analysis, CRC Press, Boca Raton, FL, (1997), 225–302.

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  103. M. M. Rao Nonlinear prediction with increasing loss. J. N. Srivastava: felicitation volume. J. Combin. Inform. System Sci. 23 (1998), no. 1–4, 187–192.

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  104. M. M. Rao Characterizing covariances and means of harmonizable processes. Infinite Dimensional Analysis and Quantum Probability, Kyoto (2000), 363–381.

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  105. M. M. Rao Multidimensional Orlicz space interpolation with changing measures. Peetre 65 Proceedings, Lund, Sweden, (2000).

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  106. M. M. Rao Representations of conditional means. Dedicated to Professor Nicholas Vakhania on the occasion of his 70th birthday. Georgian Math. J. 8 (2001), no. 2, 363–376.

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  107. M. M. Rao Convolutions of vector fields. II. Random walk models. Proceedings of the Third World Congress of Nonlinear Analysts, Part 6 (Catania, 2000). Nonlinear Anal. 47 (2001), no. 6, 3599–3615.

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  108. M. M. Rao Martingales and some applications. Shanbhag, D. N. (ed.) et al., Stochastic processes: Theory and methods. Amsterdam: North-Holland/Elsevier. Handbook Statistics 19, (2001) 765–816.

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  109. M. M. Rao Probability (revised and expanded for 3rd ed.), Encyclopedia of Physical Science and Technology (2002), pp. 87–109.

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  110. M. M. Rao Representation and estimation for harmonizable type processes. IEEE, (2002) 15591564.

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  111. M. M. Rao A commentary on “Une Théorie Unifiée des martingales et des moyennes ergodigues”, C.R. Acad. Sci 252 (1961) p. 2064–2066, in Rota’s Saleta, Birkhauser Boston (2002)

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  112. M. M. Rao Evolution operators in stochastic processes and inference. Evolution Equation, G. R. Goldstein, R. Nagel, S. Romanelli, editors, Marcel Dekker Inc. (2003), 357–372.

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  113. M. M. Rao Stochastic analysis and function spaces. Recent Advances in Stochastic Processes and Functional Analysis, A.C. Krinik, R.J. Swift, editors, Marcel Dekker Inc. (2004), 1–25.

  114. M. M. Rao Convolutions of vector fields. III. Amenability and spectral properties. Real and stochastic analysis, (2004), 375–401.

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  115. M. M. Rao Characterizations of harmonizable fields. Nonlinear Anal. 63 (2005), no. 5–7, 935–947.

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  116. M. M. Rao Structure of Karhunen processes. J. Comb. Inf. Syst. Sci. 31 (2006), no. 1–4, 187–207.

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  117. M. M. Rao Exploring ramifications of the equation E(Y = X) = X. J. Stat. Theory Pract. 1 (2007), no. 1, 73–88.

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  118. M. M. Rao Integral representations of second order processes. Nonlinear Anal. 69 (2008), no. 3, 979–986.

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  119. M. M. Rao Random measures and applications. Stoch. Anal. Appl. 27 (2009), no. 5, 1014–1076.

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  120. M. M. Rao Quadratic equations in Hilbertian operators and applications. Internat. J. Math. 20 (2009), no. 11, 1431–1454. (with V.J. Mizel)

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  121. M. M. Rao Linear regression for random measures. Advances in multivariate statistical methods, (2009), 131–144.

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  122. M. M. Rao Applications and aspects of random measures. Nonlinear Anal. 71 (2009), 1513–1518.

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Books Edited

  1. M. M. Rao General Topology and Modern Analysis. Proceedings of the F.B. Jones Conference, Academic Press, Inc., New York (1981), 514 pages, (Edited jointly with L.F. McCauley).

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  2. M. M. Rao Handbook in Statistics, Volume 5, Time Series in the Time Domain, (Edited jointly with E.J. Hannan, P.R. Krishnaiah), North-Holland Publishing Co., Amsterdam (1985).

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  3. M. M. Rao Real and Stochastic Analysis, (Editor), Wiley & Sons, New York (1986), 347 pages.

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  4. M. M. Rao Multivariate Statistics and Probability, (Edited jointly with C.R. Rao), Academic Press Inc., Boston (1989), 565 pages.

  5. M. M. Rao Real and stochastic analysis. Recent advances. (Editor) Boca Raton, FL, CRC Press. (1997), 393 pages.

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  6. M. M. Rao Real and stochastic analysis. New Perspectives. (Editor) Birkhauser Boston, MA, (2004), 405 pages.

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Books Written

  1. M. M. Rao Stochastic Processes and Integration. Sijthoff & Noordhoff International Publishers, Alpehn aan den Rijn, The Netherlands, (1979), 460 pages.

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  2. M. M. Rao Foundations of Stochastic Analysis, Academic Press, Inc., New York, (1981), 295 pages. Reprinted by Dover Publications, (2011).

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  3. M. M. Rao Probability Theory with Applications, Academic Press, Inc. New York, (1984), 495 pages.

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  4. M. M. Rao Measure Theory and Integration, Wiley-Interscience, New York (1987), 540 pages.

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  5. M. M. Rao Theory of Orlicz Spaces (jointly with Z. D. Ren), Marcel Dekker Inc., New York (1991), 449 pages.

  6. M. M. Rao Conditional Measures and Applications, Marcel Dekker Inc., New York (1993), 417 pages.

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  7. M. M. Rao Stochastic Processes: General Theory, Kluwer Academic Publishers, The Netherlands (1995), 620 pages.

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  8. M. M. Rao Stochastic Processes: Inference Theory, Kluwer Academic Publishers, The Netherlands (2000), 645 pages.

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  9. M. M. Rao Applications of Orlicz Spaces (jointly with Z. D. Ren), Marcel Dekker Inc., New York (2002), 464 pages.

  10. M. M. Rao Measure Theory and Integration, (Revised and enlarged second edition), Marcel Dekker, Inc., New York, (2004), 761 pages.

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  11. M. M. Rao Conditional Measures and Applications, (Revised second edition), Chapman & Hall/CRC, Boca Raton, FL, (2005), 483 pages.

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  12. M. M. Rao Probability Theory with Applications, (jointly with R. J. Swift), (Revised and enlarged second edition), Springer, New York, (2006), 527 pages.

  13. M. M. Rao Random and Vector Measures, World Scientific, Singapore, (2011), 550 pages.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, California State Polytechnic University, Pomona, CA, 91768, USA

    Michael L. Green, Alan C. Krinik & Randall J. Swift

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  1. Michael L. Green
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  2. Alan C. Krinik
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  3. Randall J. Swift
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Green, M.L., Krinik, A.C. & Swift, R.J. The Life and Work of M. M. Rao. J Stat Theory Pract 5, 537–545 (2011). https://doi.org/10.1080/15598608.2011.10412045

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