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

Bessaih, H, Schurz, H. (2007). Upper bounds on the rate of convergence of truncated stochastic infinite-dimensional differential systems with H-regular noise . JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 208(2), 354-361. 10.1016/j.cam.2006.10.003

cited authors

  • Bessaih, H; Schurz, H

authors

abstract

  • The rate of H-convergence of truncations of stochastic infinite-dimensional systemsd u = [Au + B (u)] d t + G (u) d W, u (0, ·) = u0 ∈ Hwith nonrandom, local Lipschitz-continuous operators A, B and G acting on a separable Hilbert space H, where u = u (t, x) : [0, T] × D → Rd (D ⊂ Rd) 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 h (N) = ∑k = N + 1+ ∞ αn, where αn ∈ R+1 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. © 2006 Elsevier B.V. All rights reserved.

publication date

  • November 15, 2007

published in

Digital Object Identifier (DOI)

start page

  • 354

end page

  • 361

volume

  • 208

issue

  • 2