Upper bounds on the rate of convergence of truncated stochastic infinite-dimensional differential systems with H-regular noise

Authors:
H. Bessaih;H. Schurz
Affiliations:
Department of Mathematics, University of Wyoming, 1000 East University Avenue, Laramie, WY 82071-3036, USA;Department of Mathematics, Southern Illinois University, 1245 Lincoln Drive, Carbondale, IL 62901-4408, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

The rate of H-convergence of truncations of stochastic infinite-dimensional systems with nonrandom, local Lipschitz-continuous operators A,B and G acting on a separable Hilbert space H, where is studied. For this purpose, some new kind of monotonicity conditions on those operators and an existing H-series expansion of the Wiener process W are exploited. The rate of convergence is expressed in terms of the converging series-remainder , where are the eigenvalues of the covariance operator Q of W. An application to the approximation of semilinear stochastic partial differential equations with cubic-type of nonlinearity is given too.