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Stochastic integrals in an arbitrary probability gauge space

Published online by Cambridge University Press:  24 October 2008

C. Barnett ,
R. F. Streater  and
I. F. Wilde
C. Barnett
Affiliation:
Department of Mathematics, Bedford College, Regent's Park, London NW1 4NS
R. F. Streater
Affiliation:
Department of Mathematics, Bedford College, Regent's Park, London NW1 4NS
I. F. Wilde
Affiliation:
Department of Mathematics, Bedford College, Regent's Park, London NW1 4NS
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Extract

In § 7 of [1] we described how a stochastic integral of non-commuting process cesan be constructed. This was achieved via a Doob-Meyer decomposition for the square of a self-adjoint L2-martingale. We introduced a ‘condition D'’ derived from the lsquo;class D’ of stochastic process theory, and showed that if the square of a self-adjoint L2-martingale satisfies this condition then it has a decomposition of the Doob-Meyer type. The purpose of this paper is to extend the results of § 7 of [1] and to introduce another construction of the stochastic integral that does not employ condition D.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 541 - 551
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

[1] Barnett, C., Streater, R. F. and Wilde, I. F.. The Ito Clifford integral. J. Funct. Anal. 48 (1982), 172–212.CrossRefGoogle Scholar
[2] Barnett, C.. Supermartingales on semifinite von Neumann algebras. J. London Math. Soc. (2) 24 (1981), 175–181.CrossRefGoogle Scholar
[3] Bartle, R. G.. A general bilinear vector integral. Studia Math. 15 (1956), 337–352.CrossRefGoogle Scholar
[4] kopp, P. E.. Martingales and Stochastic Integrals. (Cambridge University Press, 1984).CrossRefGoogle Scholar
[5] Yeadon, F. J.. Non-commutative L 9 spaces. Math. Proc. Cambridge Philon. Soc. 77 (1975), 91–102.CrossRefGoogle Scholar