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

• Published in: Journal of mathematical analysis and applications 2007-08, Vol.332 (1), p.334-345
• Main Author: Schurz, H.
• Format: Article
• Language: English
• Subjects: Approximate strong solutions; Exact sciences and technology; Existence and uniqueness; Functional analysis; Functions of a complex variable; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Ordinary differential equations; Sciences and techniques of general use; Space–time noise; Stochastic evolution equations; Stochastic infinite-dimensional systems; Stochastic partial differential equations; Strong solutions
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2006.10.012

Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systems d u = [ A ( t ) u + B ( t , u ) ] d t + G ( t , u ) d W , u ( 0 , ⋅ ) = u 0 ∈ 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–time Wiener process W ( U-valued, U ⊆ H , U Hilbert space) with ∑ n = 1 + ∞ α n 2 < + ∞ belonging to the trace of related covariance operator Q of W with local noise intensities α n 2 ∈ R 1 as eigenvalues of Q are exploited.