Almost automorphic solutions for stochastic differential equations driven by Lévy noise

By Zhi Li, Liping Xu. Physica A: Statistical Mechanics and its Applications, 2020

57 citations recorded by the source corpus.

Abstract In this paper, we are concerned with almost automorphic solutions for semilinear stochastic differential equations driven by Levy noise on the Hilbert space. We present a new variant of Gronwall’s lemma which improves the variant of Gronwall’s lemma in Kamenskii (2015). Based on this new variant of Gronwall’s lemma, suitable conditions on the coefficients, we prove the existence and uniqueness of almost automorphic solution in distribution for some stochastic differential equations driven by Levy noise on the Hilbert space, which improves and generalizes the results in Liu (2014). Subsequently, by using this new variant of Gronwall’s lemma, we investigate the existence and uniqueness of almost automorphic solution in distribution for stochastic differential equations driven by Levy noise with Markov switching processes under some weaker conditions. In the end, two examples are given to illustrate the theoretical results obtained in this paper.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/31a298ac27ea527ff984ce54f58f6acca9ee5e91