Advertisement

Multidimensional quantum diffusions

  • M. Evans
  • R. L. Hudson
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1303)

Keywords

Stochastic Differential Equation Injective Homomorphism Cohomology Space Quantum Diffusion Coboundary Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Accardi, L., Frigerio, A. and Lewis, J.T., Quantum stochastic processes, Proc. Res. Inst. Math. Sci. Kyoto 18, 94–133 (1982).MathSciNetzbMATHGoogle Scholar
  2. [2]
    Applebaum, D.B. and Hudson, R.L., Fermion Ito's formula and stochastic evolutions, Commun. Math. Phys. 96, 473–496 (1984).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Applebaum, D.B. and Hudson, R.L., Fermion diffusions, J. Math. Phys. 25, 858–61 (1984).MathSciNetCrossRefGoogle Scholar
  4. [4]
    Connes, A, Noncommutative differential geometry, Publ. IHES 62, 41–144 (1985).CrossRefzbMATHGoogle Scholar
  5. [5]
    Connes, A and M. Rieffel, Yang Mills for noncommutative two tori (preprint).Google Scholar
  6. [6]
    Elworthy, K.D., Stochastic differential equations on manifolds, CUP (1982).Google Scholar
  7. [7]
    M. Evans, Nottingham thesis in preparation.Google Scholar
  8. [8]
    Hochschild, G., On the cohomology groups of an associative algebra, Ann. of Math. 48, 326–341 (1945).MathSciNetzbMATHGoogle Scholar
  9. [9]
    Hudson, R.L., Quantum diffusions and cohomology of algebras, to appear in Proceedings of 1st World Congress of Bernoulli Society, Tashkent 1986.Google Scholar
  10. [10]
    Hudson, R.L., Algebraic theory of quantum diffusions, to appear in Stochastic differential equations, Proceedings, Swansed 1986, ed. A. TrumanGoogle Scholar
  11. [11]
    Hudson, R.L. and Parthasarathy, K.R., Quantum Diffusions, in Theory and Applications of Random Fields, Proceedings, Bangalore 1982, ed. Kallianpur, Springer LN Control Theory and Inf. Sci. 49 (1983).Google Scholar
  12. [12]
    Hudson, R.L. and Parthasarathy, K.R., Construction of quantum diffusions, in Quantum probability and applications to quantum theory of irreversible processes, proceedings Rome 1982. ed. Accardi L, Frigerio, A. and Gorini V. Springer LNM 1055 (1984).Google Scholar
  13. [13]
    Hudson, R.L. and Parthasarathy, K.R., Quantum Ito's formula and stochastic evolutions, Commun. Math. Phys. 93, 301–323 (1984).MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Ikeda, N. and Watanabe, S., Stochastic differential equations and diffusion processes, North Holland (1981).Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Evans
    • 1
  • R. L. Hudson
    • 1
  1. 1.Mathematics DepartmentNottingham UniversityNottinghamUK

Personalised recommendations