Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T14:37:40.023Z Has data issue: false hasContentIssue false
  • English
  • Français

Stopping non-commutative processes

Published online by Cambridge University Press:  24 October 2008

Chris Barnett  and
Terry Lyons
Chris Barnett
Affiliation:
Department of Mathematics, Imperial College, London SW7
Terry Lyons
Affiliation:
Department of Mathematics, Imperial College, London SW7
Get access Rights & Permissions [Opens in a new window]

Extract

Stopping times are a powerful tool in the theory of stochastic processes, so it is natural to ask whether they have a counterpart in the theory of non-commutative processes. This paper is a part answer to that question. We show that the ‘formalism’ of stopping times carries over to a non-commutative context and prove an Optional Stopping Theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 151 - 161
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Barnett, C.. Ph.D. Thesis, Hull University, 1980.Google Scholar
[2]Barnett, C.. Averaging operators in non-commutative Lp Spaces. I. Glasgow Math. J. 24 (1983), 71–74.CrossRefGoogle Scholar
[3]Barnett, C., Streater, R. F. and Wilde, I. F.. The Itô-Clifford integral. J. Functional Analysis 48 (1982), 172–212.CrossRefGoogle Scholar
[4]Barnett, C., Streater, R. F. and Wilde, I. F.. The Itô-Clifford integral: IV. J. Operator Theory 11 (1984), 255–271.Google Scholar
[5]Barnett, C., Streater, R. F. and Wilde, I. F.. Quantum stochastic integrals under standing hypothesis (Preprint).Google Scholar
[6]Cuculescu, I.. Martingales on von Neumann algebras. J. Multivariate Analysis 1, 1971, 17–27.CrossRefGoogle Scholar
[7]Dunford, N. and Schwartz, J. T.. Linear Operators, Part I (Wiley, 1958).Google Scholar
[8]Dunford, N. and Schwartz, J. T.. Linear Operators, Part II (Wiley, 1958).Google Scholar
[9]Hudson, R. L.. The strong Markov property for canonical Wiener processes. J. Functional Analysis 34 (1979), 266–281.CrossRefGoogle Scholar
[10]Kussmaul, A.. Stochastic Integration and Generalised Martingales. Research Notes in Mathematics (Pitman, 1977).Google Scholar
[11]McShane, E. J.. Stochastic Calculus and Stochastic Models (Academic Press, 1974).Google Scholar