Stability of stochastic functional differential equations and the W-transform
Date
2004-07-27
Authors
Kadiev, Ramazan
Ponosov, Arcady
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
The paper contains a systematic presentation of how the so-called "W-transform'' can be used to study stability of stochastic functional differential equations. The W-transform is an integral transform which typically is generated by a simpler differential equation ("reference equation'') via the Cauchy representation of its solutions ("variation-of-constant formula''). This other equation is supposed to have prescribed asymptotic properties (in this paper: Various kinds of stability). Applying the W-transform to the given equation produces an operator equation in a suitable space of stochastic processes, which depends on the asymptotic property we are interested in. In the paper we justify this method, describe some of its general properties, and illustrate the results by a number of examples.
Description
Keywords
Stability, Stochastic differential equations with aftereffect, Integral transforms
Citation
Kadiev, R., & Ponosov, A. (2004). Stability of stochastic functional differential equations and the W-transform. <i>Electronic Journal of Differential Equations, 2004</i>(92), pp. 1-36.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.