Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4622661 | Journal of Mathematical Analysis and Applications | 2007 | 12 Pages |
Abstract
Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systemsdu=[A(t)u+B(t,u)]dt+G(t,u)dW,u(0,⋅)=u0∈H,t⩾0 with local Lipschitz-continuous, time-depending nonrandom operators A,BA,B and G acting on a separable Hilbert space H are studied. For this purpose, some monotonicity conditions on those operators and an existing U-series expansion of the space–time Wiener process W (U -valued, U⊆HU⊆H, U Hilbert space) with ∑n=1+∞αn2<+∞ belonging to the trace of related covariance operator Q of W with local noise intensities αn2∈R1 as eigenvalues of Q are exploited.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
H. Schurz,