 Uniform stability of autonomous linear stochastic functional differential equations in infinite dimensionsKai Liu Stochastic Processes and their Applications, 2005, vol. 115, issue 7, 1131-1165 Abstract: Existence, uniqueness and continuity of mild solutions are established for stochastic linear functional differential equations in an appropriate Hilbert space which is particularly suitable for stability analysis. An attempt is made to obtain some infinite dimensional stochastic extensions of the corresponding deterministic stability results. One of the most important results is to show that the uniformly asymptotic stability of the equations we try to handle is equivalent to their square integrability in some suitable sense. Subsequently, the stability results derived in retarded case are applied to coping with stability for a large class of neutral linear stochastic systems. Keywords: Linear; stochastic; functional; differential; equations; Neutral; linear; stochastic; functional; differential; equations; Uniform; L2-stability; in; mean; square (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:115:y:2005:i:7:p:1131-1165 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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