Skip to main content

Bernoulli fields

  • Conference paper
  • First Online:
Quantum Probability and Applications IV

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

  • 475 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Luigi Accardi Wilhelm von Waldenfels

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics