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Existence of almost periodic solutions to some stochastic differential equations. (English) Zbl 1130.34033
The concept of \(p\)th-mean almost periodicity for Banach-space-valued stochastic processes is studied. Some preliminary results are applied to verify existence and uniqueness of mean-square almost periodic mild solutions for semilinear stochastic evolution equations \[ dX(t) = [ A X(t) + F(t,X(t)) ] dt + G(t,X(t)) dW(t) \] with mean-square periodic, Lipschitz-continuous nonlinearity \(F\) and driven by Brownian motion \(W\). For this purpose, they make use of well-known Banach’s fixed point principle.

34F05 Ordinary differential equations and systems with randomness
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
35B15 Almost and pseudo-almost periodic solutions to PDEs
37L55 Infinite-dimensional random dynamical systems; stochastic equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60H25 Random operators and equations (aspects of stochastic analysis)
Full Text: DOI
[1] Arnold L, Stochastics and Stochastic Reports 64 pp 177– (1998) · Zbl 1043.60513 · doi:10.1080/17442509808834163
[2] Corduneanu C, Almost Periodic Functions, 2. ed. (1989)
[3] Da Prato D, Stochastic Analaysis and Applications 13 (1) pp 13– (1995) · Zbl 0816.60062 · doi:10.1080/07362999508809380
[4] Dorogovtsev A.Ya., Kiivsćkogo Universitetu Seriya Matematikita Mekhaniki 30 pp 21– (1988)
[5] Kawata T, Statistics and Probability: Essays in Honor of C. R. Rao pp 383– (1982)
[6] Luo J, Journal of Computational and Applied Mathematics 196 (1) pp 87– (2006) · Zbl 1097.60049 · doi:10.1016/j.cam.2005.08.023
[7] Slutsky E, Actualités Sceintifiques et industrielles 738 pp 33– (1938)
[8] Swift RJ, Georgian Mathematical Journal 3 (3) pp 275– (1996) · Zbl 0854.60036 · doi:10.1007/BF02280009
[9] Tudor C, Stochastics and Stochastic Reports 38 pp 251– (1992) · Zbl 0752.60049 · doi:10.1080/17442509208833758
[10] Udagawa M, Rep. Statist. Appl. Res. Union Jap. Sci. Eng. 2 (23) pp 1– (1952)
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