Skip to main content
SpringerLink
Log in

Quantum stochastic processes

  • Conference paper
  • First Online:
Quantum Probability and Applications to the Quantum Theory of Irreversible Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1055))

  • 574 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. I.E. Segal. Mathematical Problems of Relativistic Physics. Publ. Amer. Math. Soc. 1962.

    Google Scholar 

  2. R.F. Streater: Current Commutation Relations, Continuous Tensor Products, and Infinitely Divisible Group Representations. In Local Quantum Theory (R. Jost, Ed.), Academic Press, 1969.

    Google Scholar 

  3. A.M. Cockroft and R.L. Hudson: Quantum Mechanical Wiener Processes. J. Multivariate Anal. 7, 107–123 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Hida: Brownian Motion, Springer-Verlag, 1980.

    Google Scholar 

  5. C. Barnett, R.F. Streater and I.F. Wilde. The Ito-Clifford Integral. J. Funct. Anal. 48, 172–212 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  6. I.F. Wilde. The Free Fermion field as a Markov field. J. Funcl. Anal. 15, 12–21 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  7. C. Barnett, R.F. Streater and I.F. Wilde. The Ito-Clifford Integral III — A Markov Property. Commun. Maths. Phys. (to appear).

    Google Scholar 

  8. R.F. Streater. Damped Oscillator with Quantum Noise. J. Phys. A., 15, 1477–1485 (1982).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. G.W. Ford, M. Kac and P. Mazur: Statistical Mechanics of coupled oscillators. J. Math. Phys. 6, 504–515 (1965).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. J.T. Lewis and L. Thomas, How to make a heat bath. In Functional Integration and its Applications. Ed. A.M. Arthurs. Clarendon Press, Oxford 1975. See also: Ann. Inst. Henri Poincaré A22, 241–248 (1975).

    Google Scholar 

  11. R.F. Streater and A.S. Wightman. PCT, Spin and Statistics and All That, Benjamin-Cummings, 2nd Ed.

    Google Scholar 

  12. G.C. Emch. Non-equilibrium quantum statistical mechanics, in: Current Problems in Elementary Particle and Mathematical Physics. P. Urban, Ed. Springer 1976.

    Google Scholar 

  13. R.L. Hudson and R.F. Streater. Non-commutative martingales and stochastic integrals in Fock space. In: Stochastic Processes in Quantum Theory and Statistical Physics. (Ed. S. Albeverio, Ph. Combe and M. Sirugue Collin). Lecture Notes in Physics 173. Springer 1981.

    Google Scholar 

  14. D.E. Evans; Completely positive quasi-free maps of the CAR algebra. Commun. Math. Phys. 70, 53–68 (1979).

    Article  ADS  MATH  Google Scholar 

  15. D.E. Evans and J.T. Lewis: Dilations of irreversible evolutions in algebraic quantum theory. Commun. of Dublin Institute of Advanced Studies A24, 1977.

    Google Scholar 

  16. R.L. Hudson and R.F. Streater. Examples of Quantum Martingales. Phys. Lett. A85, 64–67 (1981). Ito's Formula is the Chain rule with Wick Ordering. Ibid, A86, 277–279 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  17. C. Barnett, Supermartingales on semi-finite von Neumann algebras. J. London Math. Soc. (2) 24, 175–181 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  18. A. Kussmaul. Stochastic integration and generalized martingales. Research Notes in Mathematics. Pitman, London 1977.

    MATH  Google Scholar 

  19. C. Barnett, R.F. Streater and I.F. Wilde. Quantum Stochastic Integrals under Standing Hypotheses. Submitted to Z. fur. Wahrsch.

    Google Scholar 

  20. E.J. McShane. Stochastic calculus and stochastic models. Academic Press 1974.

    Google Scholar 

  21. C. Barnett, R.F. Streater and I.F. Wilde. Decomposition and Stochastic Integrals in an arbitrary probability gauge space, to appear.

    Google Scholar 

  22. C. Barnett, R.F. Streater and I.F. Wilde. Quasi-free quantum stochastic integrals for the CAR and CCR. Submitted to J. Funcl. Anal.

    Google Scholar 

  23. C. Barnett, R.F. Streater and I.F. Wilde, The Ito-Clifford Integral IV: A Radon-Nikodym Theorem and Bracket Process. Submitted to J. Operator Theory.

    Google Scholar 

  24. C. Barnett, R.F. Streater and I.F. Wilde. The Ito-Clifford Integral II: Stochastic Differential Equations. J. Lond. Math. Soc. (2), 27, 373–384 (1983).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bedford College, USA

    C. Barnett, R. F. Streater & I. F. Wilde

Authors
  1. C. Barnett
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. F. Streater
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. F. Wilde
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Luigi Accardi Alberto Frigerio Vittorio Gorini

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Barnett, C., Streater, R.F., Wilde, I.F. (1984). Quantum stochastic processes. In: Accardi, L., Frigerio, A., Gorini, V. (eds) Quantum Probability and Applications to the Quantum Theory of Irreversible Processes. Lecture Notes in Mathematics, vol 1055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071708

Download citation

  • DOI: https://doi.org/10.1007/BFb0071708

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12915-8

  • Online ISBN: 978-3-540-38798-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation