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Moments of certain stochastic integrals occurring in mathematical physics

Published online by Cambridge University Press:  14 November 2011

Lieven Smits
Lieven Smits
Affiliation:
Departement Wiskunde, Universiteit Antwerpen (UIA), Universiteitsplein 1, 2610 Wilrijk, Belgium
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Synopsis

We give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.

We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 3-4 , 1992 , pp. 267 - 282
Copyright
Copyright © Royal Society of Edinburgh 1992

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