Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with H-regular noise

Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systems du = 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,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–timeWiener process W (U-valued, U ⊆ H, U Hilbert space) with +∞ n=1 α2 n <+∞ belonging to the trace of related covariance operator Q of W with local noise intensities α2 n ∈ R1 as eigenvalues of Q are exploited. © 2006 Elsevier Inc. All rights reserved.