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Bernoulli fields

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1396)

Keywords

  • Hilbert Space
  • Orthogonal Polynomial
  • Stochastic Integral
  • Springer Lecture Note
  • Reduce Matrix Element

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References

  1. L. Accardi and K.R. Parthasarathy, Stochastic calculus on local algebras, Springer Lecture Notes in Math., 1136(1985) 9–23.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. A. Boukas, Quantum stochastic calculus, a non-Brownian case, Ph.D. Dissertation, SIU, 1988.

    Google Scholar 

  3. C. Barnett, R. F. Streater, and I. F. Wilde, The Ito-Clifford Integral, J. Fl. Analysis 48(1982), 172–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. T.S. Chihara, An introduction to orthogonal polynomials, Mathematics and Applications Series, 13, Gordon and Breach, 1978.

    Google Scholar 

  5. M. Emery, Stabilité des solutions des équations différentielles stochastiques, application aux intégrales multiplicatives stochastiques, Z. Wahrsch. Verw. Gebiete 41(1978), 241–262.

    CrossRef  MATH  Google Scholar 

  6. P. Feinsilver, Lie algebras and recurrence relations I, submitted to Acta Applicandae Math., 1988.

    Google Scholar 

  7. P. Feinsilver, Some classes of orthogonal polynomials associated with martingales, Proceedings of the AMS. 98, 2(1986), 298–302.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. P. Feinsilver, Bernoulli systems in several variables, Conference Proceedings, Probability Measures on Groups, Springer Lecture Notes, Vol. 1064 (1984), 86–98.

    MathSciNet  MATH  Google Scholar 

  9. P. Feinsilver, Canonical representation of the Bernoulli process, Conference Proceedings, Probability Measures on Groups, Oberwolfach. Germany, Springer Lecture Notes, Vol. 928, (1982), 90–95.

    MathSciNet  Google Scholar 

  10. P. Feinsilver, Special functions, probability semigroups, and Hamiltonian flows, Lecture Notes in Math., 696, 1978.

    Google Scholar 

  11. P. Feinsilver, Operator calculus, Pacific J. Mathematics, Vol. 78, No. 1 (1978), 95–116.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. A. Guichardet, Symmetric Hilbert spaces and related topics, Lect. Notes in Math., 261, Springer-Verlag, 1972.

    Google Scholar 

  13. J. Meixner, Orthogonale polynomsysteme mit einem besonderen gestalt der erzeugenden funktion, J. London Math. soc., 9, 6–13, 1934.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. K.R. Parthasarathy and R.L. Hudson, Quantum Itô's formula, Comm. Math. Phys. 93(1984), 301–323.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. K.R. Parthasarathy and K. Schmidt, Positive definite kernels, continuous tensor products, and central limit theorems of probability theory, Lecture Notes-Mathematics, 272, Springer-Verlag, 1972.

    Google Scholar 

  16. F. Pollaczek, Sur une famille de polynômes orthogonaux qui contient let polynômes d'Hermite et de Laguerre comme cas limites, Comptes Rend. Acad. Sci., Paris, 230(1950), 1563–1565.

    MathSciNet  MATH  Google Scholar 

  17. G.-C. Rota, Finite operator calculus, Academic Press, 1975.

    Google Scholar 

  18. R.F. Streater, Euclidean quantum mechanics and stochastic integrals, in London Math. Soc, 1980, Durham symposium, Stochastic Integrals. Lecture Notes in Math. 851, Springer-Verlag.

    Google Scholar 

  19. R.F. Streater and A. Wulfsohn, Continuous tensor products of Hilbert spaces and generalized random fields, Nuovo Cimento, B 10, 57 (1968) 330–339.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. R.O. Wells, Jr., Differential analysis on complex manifolds, Prentice-Hall, 1973.

    Google Scholar 

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© 1989 Springer-Verlag

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Feinsilver, P. (1989). Bernoulli fields. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083552

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  • DOI: https://doi.org/10.1007/BFb0083552

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

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