Almost automorphy and various extensions for stochastic processes
Probability
2015-04-21 v3 Dynamical Systems
Abstract
We compare different modes of pseudo almost automorphy and variants for stochastic processes: in probability, in quadratic mean, or in distribution in various senses. We show by a counterexample that square-mean (pseudo) almost automorphy is a property which is too strong for stochastic differential equations (SDEs). Finally, we consider two semilinear SDEs, one with almost automorphic coefficients and the second one with pseudo almost automorphic coefficients, and we prove the existence and uniqueness of a mild solution which is almost automorphic in distribution in the first case, and pseudo almost automorphic in distribution in the second case.
Cite
@article{arxiv.1412.5032,
title = {Almost automorphy and various extensions for stochastic processes},
author = {Fazia Bedouhene and Nouredine Challali and Omar Mellah and Paul Raynaud de Fitte and Mannal Smaali},
journal= {arXiv preprint arXiv:1412.5032},
year = {2015}
}