A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions

Yong Ren, Tingting Hou, R. Sakthivel and Xing Cheng

Applied Mathematics and Computation, 2014, vol. 232, issue C, 658-665

Abstract: In this note, we aim to study a class of second-order non-autonomous neutral stochastic evolution equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion with Hurst parameter H∈(1/2,1), in which the initial value belongs to the abstract space B. We establish the existence and uniqueness of mild solutions for this kind of equations under some Carathéodory conditions by means of the successive approximation. The obtained result extends some well-known results. An example is proposed to illustrate the theory.

Keywords: Second-order neutral stochastic evolution equation; Non-autonomous; Infinite delay; Carathéodory condition (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:658-665

DOI: 10.1016/j.amc.2014.01.091

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