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

摘要

The rate of H-convergence of truncations of stochastic infinite-dimensional systemsdu=[Au+B(u)]dt+G(u)dW,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.