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Stochastic Fubini Theorem for Semimartingales in Hilbert Space

Published online by Cambridge University Press:  20 November 2018

Jorge A. León
Jorge A. León*
Affiliation:
Centro de Investigación y de Estudios Avanzandos, Departamento de Matemáticas, Apartado postal 14-740, México 07000 D. F., México
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In this paper we will study the Fubini theorem for stochastic integrals with respect to semimartingales in Hilbert space.

Let (Ω, , P) he a probability space, (X, , μ) a measure space, H and G two Hilbert spaces, L(H, G) the space of bounded linear operators from H into G, Z an H-valued semimartingale relative to a given filtration, and φ: X × R+ × Ω → L(H, G) a function such that for each t ∈ R+ the iterated integrals are well-defined (the integrals with respect to μ are Bochner integrals). It is often necessary to have sufficient conditions for the process Y1 to be a version of the process Y2 (e.g. [1], proof of Theorem 2.11).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 890 - 901
Copyright
Copyright © Canadian Mathematical Society 1990

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