Weak infinitesimal generator for a stochastic partial differential equation with time delay. (1995)

• Record Type: Journal Article
• Authors: Chang, Mou-Hsiung
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 8:Number 2(1995)
• Page Start: 115
• Page End: 138
• Publication Date: 1995
• Subjects: stochastic partial differential equation with time delay -- Markov operators -- weak infinitesimal generator; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953395000128
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In this paper, we consider the Markov solution process for a stochastic parabolic differential equation with time delay. Under the Lipschitz condition and boundedness on the drift and diffusion coefficient, properties of the weak infinitesimal generator of the associated Markov operators are established. Actions of the weak infinitesimal generator on the space of quasi-tame functions are also investigated.