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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 |
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Dang Hung Thang and Nguyen Thinh |
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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 $C^2$-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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