Stationary and almost periodic solutions of almost periodic affine stochastic differential equations

RETRACTED ARTICLE: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

“…Lemma 2.1 (see [25] In [26], the authors also got the explicit solution of the following special type of NSD equation.…”

Existence of almost periodic solutions to some stochastic differential equations

“…The previous basic results, especially Theorem 2.7, are, subsequently, applied to studying the existence and uniqueness of a square-mean almost periodic solution to semilinear stochastic equations on L 2 ðP, HÞ where H is a real separable Hilbert space (Theorem 3.2). One should point that several contributions upon the study of almost periodic solutions to stochastic differential equations can be found in the literature, see, e.g., [1,3,9]. Here, we essentially make use of the Banach fixedpoint principle to obtain the existence and uniqueness of a square-mean almost periodic solution to (3.1).…”

“…The concept of almost periodicity is important in probability for investigating stochastic processes [1][2][3][4][5]8,9]. Such a notion is also of interest for applications arising in mathematical physics and statistics.…”

Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion

“…Therefore, we must import the stochastic effects into the investigation of differential systems. Since 1980s, almost periodic solutions to stochastic differential equations (SDEs) driven by Gaussian motion have been studied by some authors, see Tudor (1992) and Da Prato and Tudor (1995) for the periodic and almost periodic solution in the distribution sense for stochastic evolution equations, Arnold and Tudor (1998) for the almost periodic solution in the distribution sense for stochastic ordinary affine equations. Moreover, Bezandry and Diagana (2011) introduced square-mean almost periodic solution for some SDEs.…”