Stepanov-Like Pseudo Almost Automorphic Solutions to Some Stochastic Differential Equations

In this paper, we introduce a new concept of S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-pseudo almost automorphy for stochastic processes. We apply the results obtained to investigate the existence and uniqueness of S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-pseudo almost automorphic mild solutions to some stochastic differential equations in a real separable Hilbert space. Our main results extend some known ones in the sense of square-mean pseudo almost automorphy or S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-almost automorphy for stochastic processes.