Stochastic functional differential equations of Sobolev-type with infinite delay

P. Revathi, R. Sakthivel and Yong Ren

Statistics & Probability Letters, 2016, vol. 109, issue C, 68-77

Abstract: Stochastic differential equations have been widely used to model a number of phenomena in diverse fields of science and engineering. In this paper, we focus on the local existence of mild solution for a class of stochastic functional differential equations of Sobolev-type with infinite delay. Furthermore, the results are extended to study the local existence results for neutral stochastic differential equations of Sobolev-type. Using the semigroup theory and fixed point argument, we establish a set of sufficient conditions for obtaining the required result. Furthermore, existence results for integro-differential equations of Sobolev-type is also discussed. Finally, an example is provided to illustrate the obtained theory.

Keywords: Stochastic Sobolev-type differential equation; Fixed point theorem; Mild solution; Infinite delay (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2015.10.019

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