Transformation of measures in infinite-dimensional spaces by the flow induced by a stochastic differential equation
- Institute of Mathematics of Ukrainian National Academy of Sciences, Kiev (Ukraine)
Let {mu} be a Gaussian measure in the space X and H the Cameron-Martin space of the measure {mu}. Consider the stochastic differential equation d{xi}(u,t)=a{sub t}({xi}(u,t))dt+{sigma}{sub n}{sigma}{sub t}{sup n}({xi}(u,t))d{omega}{sub n}(t), t element of [0,T]; {xi}(u,0)=u,; where u element of X, a and {sigma}{sub n} are functions taking values in H, {omega}{sub n}(t), n{>=}1 are independent one-dimensional Wiener processes. Consider the easure-valued random process {mu}{sub t}:={mu}o{xi}( {center_dot} ,t){sup -1}. It is shown that under certain natural conditions on the coefficients of the initial equation the measures {mu}{sub t}({omega}) are equivalent to {mu} for almost all {omega}. Explicit expressions for their Radon-Nikodym densities are obtained.
- OSTI ID:
- 21208310
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 4 Vol. 194; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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