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Vietnam Journal of Mathematics 33:2 (2005) 223-240

 Infinite-Dimensional Ito Processes with Respect to Gaussian Random Measures and the Ito Formula

Dang Hung Thang and Nguyen Thinh

Abstract.  In this paper, infinite-dimensional Ito processes with respect to a symmetric Gaussian random measure Z taking values in a Banach space are defined. Under some assumptions, it is shown that if X_t is an Ito process with respect to Z and g(t, x) is a C²-smooth mapping then Y_t = g(t, X_t) is again an Ito process with respect to Z. A general infinite-dimensional Ito formula is established.

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Published by Springer since January 2013