Almost automorphy and various extensions for stochastic processes
Almost automorphy and various extensions for stochastic processes
复制标题
DOI：
10.1016/j.jmaa.2015.04.014
复制
发表时间：
2014-12
影响因子：
1.3
通讯作者：
F. Bedouhene;Nouredine Challali;Omar Mellah;P. R. D. Fitte;M. Smaali
中科院分区：
文献类型：
--
作者：
F. Bedouhene;Nouredine Challali;Omar Mellah;P. R. D. Fitte;M. Smaali
我们比较了随机过程的伪几乎自同构和变异的不同模式：在概率上，在二次均值上，或在各种意义上的分布上。我们通过一个反例证明了均方根（伪）几乎自同构是随机微分方程（SDEs）的一个太强的性质。最后，我们考虑了系数近似自同构和系数伪自同构的两个半线性SDEs，证明了前者在分布上近似自同构，后者在分布上近似自同构的温和解的存在唯一性。
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.