The Craft of Probabilistic Modelling pp 166-185 | Cite as

# Return of the Wanderer: A Physicist Becomes a Probabilist

## Abstract

I grew up in New York City in the Depression. Both my parents were immigrants. My father, Jonas I. Keilson, had arrived in his late teens from Lithuania and had built up a small business as middleman between families of modest means and large merchants in lower Manhattan selling suits, overcoats, and furniture. My father provided contacts, expertise, and credit, and his business flourished. My mother, Sarah Eimer, had come as a baby from Austria. I was the third of three boys. The first, Philip, died in infancy in an accident. The second, Sidney, became an accountant and businessman. I was born on 19 November 1924. A girl, Marcia, came some nine years later and is a clinical psychologist.

### Keywords

Entropy Depression Covariance Mold Income## Preview

Unable to display preview. Download preview PDF.

### Publications and References

- [1]Abramowitz, M. and Stegun. I. A. (1965)
*Handbook of Mathematical Functions*. Dover, New York.Google Scholar - [2]Callaert, H. and Keilson, J. (1972) On exponential ergodicity and spectral structure for birth-death processes.
*Stoch. Proc. Appl.*1, 187–236.MathSciNetCrossRefGoogle Scholar - [3]Cox, D. R. (1955) The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables.
*Proc. Camb. Phil. Soc.*51, 433–441.MATHCrossRefGoogle Scholar - [4]Daniels, H. E. (1954) Saddlepoint approximations in statistics.
*Ann. Math. Statist.*25, 631–650.MathSciNetMATHCrossRefGoogle Scholar - [5]Keilson, J. (1954) A suggested modification of noise theory.
*Quart. Appl. Math.*12, 71–76.MathSciNetMATHGoogle Scholar - [6]Keilson, J. (1955) On diffusion in an external field and the adjoint source problem.
*Quart. Appl. Math.*12, 435–438.MathSciNetMATHGoogle Scholar - [7]Keilson, J. (1961) The homogeneous random walk on the half-line and the Hilbert problem.
*Bull. Inst. Internat. Statist., Proc. 33rd Session ISI, Paris*39 (2), 279–291.MathSciNetGoogle Scholar - [8]Keilson, J. (1962) The use of Green’s functions in the study of bounded random walks with application to queueing theory.
*J. Math. Phys.*41, 42–52.MathSciNetMATHGoogle Scholar - [9]Keilson, J. (1962) Non-stationary Markov walks on the lattice.
*J. Math. Phys.*41, 205–211.MathSciNetMATHGoogle Scholar - [10]Keilson, J. (1962) The general bulk queue as a Hilbert problem.
*J. R. Statist. Soc*. B 24, 344.MathSciNetMATHGoogle Scholar - [11]Keilson, J. (1962) A simple random walk and an associated asymptotic behaviour of the Bessel functions.
*Proc. Camb. Phil. Soc.*58, 708–709.MathSciNetMATHCrossRefGoogle Scholar - [12]Keilson, J. (1962) Queues subject to service interruption.
*Ann. Math. Statist.*33, 1314–1322.MathSciNetMATHCrossRefGoogle Scholar - [13]Keilson, J. (1963) A gambler’s ruin type problem in queueing theory.
*Operat. Res.*11, 570–576.MATHCrossRefGoogle Scholar - [14]Keilson, J. (1963) The first passage time density for homogeneous skip-free walks on the continuum.
*Ann. Math. Statist.*34, 375–380.MathSciNetCrossRefGoogle Scholar - [15]Keilson, J. (1963) On the asymptotic behaviour of queues.
*J. R. Statist. Soc*. B 25, 464–476.MathSciNetMATHGoogle Scholar - [16]Keilson, J. (1964) Some comments on single server queueing methods and some new results.
*Proc. Camb. Phil. Soc.*60, 237–251.MathSciNetMATHCrossRefGoogle Scholar - [17]Keilson, J. (1964) An alternative to Wiener-Hopf methods for the study of bounded processes.
*J. Appl. Prob.*1, 85–120.MathSciNetMATHCrossRefGoogle Scholar - [18]Keilson, J. (1964) On the ruin problem for the generalized random walk.
*Operat. Res.*12, 504–506.MathSciNetMATHCrossRefGoogle Scholar - [19]Keilson, J. (1964) A review of transient behavior in regular diffusion and birth-death processes.
*J. Appl. Prob.**1*, 247–266.MathSciNetMATHCrossRefGoogle Scholar - [20]Keilson, J. (1965) The role of Green’s functions in congestion theory. In
*Symp. on Congestion Theory*,University of North Carolina Press, Chapel Hill.Google Scholar - [21]Keilson, J. (1965) A review of transient behavior in regular diffusion and birth-death processes—Part II.
*J. Appl. Prob.*2, 405–428.MathSciNetMATHCrossRefGoogle Scholar - [22]Keilson, J. (1965)
*Green’s Function Methods in Probability Theory*. Griffin, London.Google Scholar - [23]Keilson, J. (1966) The ergodic queue length distribution for queueing systems with finite capacity.
*J. R. Statist. Soc*. B 28, 190–201.MathSciNetMATHGoogle Scholar - [24]Keilson, J. (1966) A limit theorem for passage times in ergodic regenerative processes.
*Ann. Math. Statist.*37, 866–870.MathSciNetMATHCrossRefGoogle Scholar - [25]Keilson, J. (1966) A technique for discussing the passage time distribution for stable systems.
*J. R. Statist. Soc*. B 28, 477–486.MathSciNetMATHGoogle Scholar - [26]Keilson, J. (1966) A theorem on optimum allocation for a class of symmetric multilinear return functions.
*J. Math. Anal. Appl.**15*, 269–272.MathSciNetMATHCrossRefGoogle Scholar - [27]Keilson, J. (1967) On global extrema for a class of symmetric functions.
*J. Math. Anal. Appl.*18, 218–228.MathSciNetMATHCrossRefGoogle Scholar - [28]Keilson, J. (1968) A note on the waiting-time distribution for the
*M/G/ l*queue with last-come-first-served discipline.*Operat. Res.*16, 1230–1232.MATHCrossRefGoogle Scholar - [29]Keilson, J. (1969) A queue model for interrupted communication.
*Opsearch*6, 59–67.MathSciNetGoogle Scholar - [30]Keilson, J. (1969) An intermittent channel with finite storage.
*Opsearch*6, 109–117.MathSciNetGoogle Scholar - [31]Keilson, J. (1969) On the matrix renewal function for Markov renewal processes.
*Ann. Math. Statist.*40, 1901–1907.MathSciNetMATHCrossRefGoogle Scholar - [32]Keilson, J. (1971) On log-concavity and log-convexity in passage-time densities of diffusion and birth-death processes.
*J. Appl. Prob.*8, 391–398.MathSciNetMATHCrossRefGoogle Scholar - [33]Keilson, J. (1971) A note on the summability of the entropy series.
*Inf. and Control*18, 257–260.MathSciNetMATHCrossRefGoogle Scholar - [34]Keilson, J. (1972) A threshold for log-concavity.
*Ann. Math. Statist.*43, 1702–1708.MathSciNetMATHCrossRefGoogle Scholar - [35]Keilson, J. (1973) Simple expressions for the mean and variance of a generalized central limit theorem and applications.
*Proc. XXth Annual Meeting, Institute of Management Science, Tel Aviv, Israel, 24–29 June**1973*, 538–541.Google Scholar - [36]Keilson, J. (1974) Sojourn times, exit times, and jitter in multivariate Markov processes.
*Adv. Appl. Prob.*6, 747–756.MathSciNetMATHCrossRefGoogle Scholar - [37]Keilson, J. (1974) Convexity and complete monotonicity in queueing distributions and associated limit behavior. In
*Mathematical Methods in Queueing Theory*, Proceedings of a Conference at Western Michigan University, 10–12 May 1974, Springer-Verlag, New York.Google Scholar - [38]Keilson, J. (1975) Systems of independent Markov components and their transient behavior. In
*Reliability and Fault Tree Analysis*, SIAM, Philadelphia, 351–364.Google Scholar - [39]Keilson, J. (1978) Exponential spectra as a tool for the study of server-systems with several classes of customers.
*J. Appl. Prob.*15, 162–170.MathSciNetMATHCrossRefGoogle Scholar - [40]Keilson, J. (1979)
*Markov Chain Models—Rarity and Exponentiality*. Applied Mathematical Sciences Series 28, Springer-Verlag, New York.Google Scholar - [41]Keilson, J. (1981) On the unimodality of passage time densities in birth-death processes.
*Statist. Neerlandica*35, 49–55.MathSciNetMATHCrossRefGoogle Scholar - [42]Keilson, J. (1982) On the distribution and covariance structure of the present value of a random income stream.
*J. Appl. Prob.*19, 240–244.MathSciNetMATHCrossRefGoogle Scholar - [43]Keilson, J. (1983) Stochastic systems (Lecture notes). Graduate School of Management, University of Rochester, Working Paper Series No. QM 8306.Google Scholar
- [44]Keilson, J. and Gerber, H. (1971) Some results for discrete unimodality.
*J. Amer. Statist. Assoc.*66, 386–390.MATHCrossRefGoogle Scholar - [45]Keilson, J. and Graves, S. C. (1979) A methodology for studying the dynamics of extended logistic systems.
*Naval Research Logist. Quart.*26, 169–197.MathSciNetMATHCrossRefGoogle Scholar - [46]Keilson, J. and Graves, S. C. (1981) The compensation method applied to a one-product production/inventory problem.
*Math. Operat. Res.*6, 246–262.MathSciNetMATHCrossRefGoogle Scholar - [47]Keilson, J. and Graves, S. C. (1983) System balance for extended logistic systems.
*Operat. Res.*31, 234–252.CrossRefGoogle Scholar - [48]Keilson, J. and Kester, A. (1977) Monotone matrices and monotone Markov processes.
*Stoch. Proc. Appl.*5, 231–241.MathSciNetMATHCrossRefGoogle Scholar - [49]Keilson, J. and Kester, A. (1977) A circulatory model for human metabolism (Unpublished monograph). Graduate School of Management, University of Rochester, Working Paper Series No. 7724.Google Scholar
- [50]Keilson, J. and Kester, A. (1978) Unimodality preservation in Markov chains.
*Stoch. Proc. Appl.*7, 179–190.MathSciNetMATHCrossRefGoogle Scholar - [51]Keilson, J. and Kooharian, A. (1960) On time-dependent queueing processes.
*Ann. Math. Statist.*31, 104–112.MathSciNetMATHCrossRefGoogle Scholar - [52]Keilson, J. and Kooharian, A. (1962) On the general time-dependent queue with a single server.
*Ann. Math. Statist.*33, 767–791.MathSciNetMATHCrossRefGoogle Scholar - [53]Keilson, J. and Kubat, P. (1984) Parts and service demand distribution generated by primary production.
*European J. Operat. Res.*17, 257–265.MathSciNetMATHCrossRefGoogle Scholar - [54]Keilson, J. and Machihara, F. (1985) Hyperexponential waiting time structure in hyperexponential
*GI/G/1*systems. Graduate School of Management, University of Rochester.Google Scholar - [55]Keilson, J. and Mermin, N. (1959) The second order distribution of integrated shot noise.
*IRE Trans. Inf. Theory*IT-5, 75–77.Google Scholar - [56]Keilson, J. and Nunn, W. (1979) Laguerre transformation as a tool for the numerical solution of integral equations of convolution type.
*Appl. Math. Comput.*5, 313–359.MathSciNetMATHCrossRefGoogle Scholar - [57]Keilson, J. and Ramaswamy, R. (1984) Convergence of quasi-stationary distributions in birth–death processes.
*Stoch. Proc. Appl.*18, 301–312.MathSciNetMATHCrossRefGoogle Scholar - [58]Keilson, J. and Ramaswamy, R. (1984) The bivariate maximum process and quasi-stationary structure in birth-death processes. Graduate School of Management, University of Rochester, Working Paper Series No. QM 8405.Google Scholar
- [59]Keilson. J. and Ross, H. F. (1975) Passage-time distributions for Gaussian Markov (Ornstein–Uhlenbeck) statistical processes.
*Selected Tables in Mathematical Statistics*3, 233–327.Google Scholar - [60]Keilson, J. and Ross, H. F. (1978) The maximum of the stationary Gaussian Markov process over an interval—Theory, table and graphs. Unpublished.Google Scholar
- [61]Keilson, J. and Ross, H. F. (1979) The maximum over an interval of meteorological variates modelled by the stationary Gaussian Markov process. Preprint volume, 6th Conference on Probability and Statistics in Atmospheric Sciences, 912 October 1979, 213–216.Google Scholar
- [62]Keilson, J. and Servi, L. (1984) Oscillating random walk models for
*GI/G/l*vacation systems with Bernoulli schedules. Graduate School of Management, University of Rochester, Working Paper Series No. QM 8403.Google Scholar - [63]Keilson, J. and Steutel, F. W. (1972) Families of infinitely divisible distributions closed under mixing and convolution.
*Ann. Math. Statist.*43, 242–250.MathSciNetMATHCrossRefGoogle Scholar - [64]Keilson, J. and Steutel, F. W. (1974) Mixtures of distributions, moment inequalities and measures of exponentiality and normality.
*Ann. Prob.*2, 112–130.MathSciNetMATHCrossRefGoogle Scholar - [65]Keilson, J. and Storer, J. E. (1952) On Brownian motion, Boltzmann’s equation and the Fokker–Planck equation.
*Quart. Appl. Math.*10, 243–253.MathSciNetMATHGoogle Scholar - [66]Keilson, J. and Styan, G. P. H. (1973) Markov chains and M-matrices: Inequalities and equalities.
*J. Math. Anal. Appl.*2, 439–459.MathSciNetCrossRefGoogle Scholar - [67]Keilson, J. and Subba Rao, S. (1970) A process with chain dependent growth rate.
*J. Appl. Prob.*7, 699–711.MathSciNetMATHCrossRefGoogle Scholar - [68]Keilson, J. and Subba Rao, S. (1971) A process with chain dependent growth rate—Part II, The ruin and ergodic problem.
*Adv. Appl. Prob.*3, 315–338.MathSciNetMATHCrossRefGoogle Scholar - [69]Keilson, J. and Sumita, U. (1982) Waiting time distribution response to traffic surges via the Laguerre transform. In
*Applied Probability—Computer Science, The Interface*2, Birkhauser, Boston.Google Scholar - [70]Keilson, J. and Sumita, U. (1982) Uniform stochastic ordering and related inequalities.
*Canad. J. Statist.*10, 181–198.MathSciNetMATHCrossRefGoogle Scholar - [71]Keilson, J. and Sumita, U. (1983) Extrapolation of the mean lifetime of a large population from its preliminary survival history.
*Naval Res. Logist. Quart.*30, 509–535.MathSciNetMATHCrossRefGoogle Scholar - [72]Keilson, J. and Sumita, U. (1983) A decomposition of the beta-distribution, related order and aymptotic behavior.
*Ann. Inst. Statist. Math*. A 35, 243–253.MathSciNetMATHCrossRefGoogle Scholar - [73]Keilson, J. and Sumita, U. (1983) The depletion time for
*M/G/1*systems and a related limit theorem.*Adv. Appl. Prob.**15*, 420–443.MathSciNetMATHCrossRefGoogle Scholar - [74]Keilson, J. and Sumita, U. (1983) Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process.
*Adv. Appl. Prob.*15, 840–856.MathSciNetMATHCrossRefGoogle Scholar - [75]Keilson, J. and Sumita, U. (1986) A general Laguerre transform and a related distance between probability measures.
*J. Math. Anal. Appl.*113, 288–308.MathSciNetMATHCrossRefGoogle Scholar - [76]Keilson, J. and Sumita, U. (1983) A time-dependent model of a two echelon system with quick repair. Graduate School of Management, University of Rochester, Working Paper Series No. QM 8311.Google Scholar
- [77]Keilson, J. and Syski, R. (1974) Compensation measures in the theory of Markov chains.
*Stoch. Proc. Appl.*2, 59–72.MathSciNetMATHCrossRefGoogle Scholar - [78]Keilson, J. and Vasicek, O. (1975) A family of monotone measures of ergodicity for Markov chains. Center for System Science 75–03, Graduate School of Management, University of Rochester.Google Scholar
- [79]Keilson, J. and Waterhouse, C. (1972) Transfer times across the human body.
*Bull. Math. Phys.*34, 33–44.Google Scholar - [80]Keilson, J. and Wellner, J. (1978) Oscillating Brownian motion.
*J. Appl. Prob.*15, 300–310.MathSciNetMATHCrossRefGoogle Scholar - [81]Keilson, J. and Wishart, D. M. G. (1964) A central limit theorem for additive processes defined on a finite Markov chain.
*Proc. Camb. Phil. Soc.*60, 657–667.MathSciNetCrossRefGoogle Scholar - [82]Keilson, J. and Wishart, D. M. G. (1965) Boundary problems for additive processes defined on a finite Markov chain.
*Proc. Camb. Phil. Soc.*61, 173–190.MathSciNetMATHCrossRefGoogle Scholar - [83]Keilson, J. and Wishart, D. M. G. (1967) Addenda to processes on a finite Markov chain.
*Proc. Camb. Phil. Soc.*63, 187–193.MathSciNetMATHCrossRefGoogle Scholar - [84]Keilson, J. and Zachmann, M. (1985) Homogeneous row-continuous bivariate Markov chains with boundaries.
*Math. Operat. Res*. To appear.Google Scholar - [85]Keilson, J., Cozzolino, J. and Young, H. (1968) A service system with unfilled requests repeated.
*Operat. Res.*16, 1126–1137.MATHCrossRefGoogle Scholar - [86]Keilson, J., Kester, A. and Waterhouse, C. (1978) A circulatory model for human metabolism.
*J. Theoret. Biol.*74, 535–547.CrossRefGoogle Scholar - [87]Keilson, J., Nunn, W. and Sumita, U. (1981) The bilateral Laguerre transform.
*Appl. Math. Comput.*8, 137–174.MathSciNetMATHCrossRefGoogle Scholar - [88]Keilson, J., Sumita, U. and Zachmann, M. (1981) Row-continuous finite Markov chains, structure and algorithms. Graduate School of Management, University of Rochester, Working Paper Series No. 8115.Google Scholar
- [89]Keilson, J., Petrondas, D., Sumita, U. and Wellner, J. (1983) Significance points for some tests of uniformity on the sphere.
*J. Statist. Comput. Simul.*17, 195–218.MathSciNetMATHCrossRefGoogle Scholar - [90]Keilson, J., Machihara, F. and Sumita, U. (1985) Spectral structure of
*M/G/1*systems—Asymptotic behavior and relaxation times. Graduate School of Management, University of Rochester, Working Paper Series No. 8414.Google Scholar - [91]Kingman, J. F. C. (1965) The heavy traffic approximation in the theory of queues. Discussion by J. Keilson and J. Th. Runnenburg, in
*Proc. Symp. Congestion Theory*, University of North Carolina Press, Chapel Hill.Google Scholar - [92]Ott, T. (1975) Infinite Divisibility, Imbeddability and Stability of Finite SemiMarkov Matrices. Doctoral Dissertation, Graduate School of Management, University of Rochester.Google Scholar
- [93]Prabhu, N. U. (1982) Conferences on Stochastic Processes and their Applications: a brief history.
*Stoch. Proc. Appl.*12, 115–116.CrossRefGoogle Scholar - [94]Wang, M. C. and Uhlenbeck, G. E. (1945) On the theory of Brownian motion II.
*Rev. Mod. Phys.*17, 323–342.MathSciNetMATHCrossRefGoogle Scholar - [95]Wax, N. (1954)
*Selected Papers on Noise and Stochastic Processes*. Dover, New York.MATHGoogle Scholar - [96]Widder, D. V. (1946)
*The Laplace Transform*. Princeton University Press, Princeton, NJ.Google Scholar - [97]Wishart, D. M. G. (1960) Queueing systems in which the discipline is ‘last-come first-served’.
*Operat. Res.*8, 591–599.MathSciNetMATHCrossRefGoogle Scholar