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Keywords:
trajectory of an almost periodic flow; uniform asymptotic stability; Itô equations; periodic and almost periodic flows; asymptotically almost periodic solution
trajectory of an almost periodic flow; uniform asymptotic stability; Itô equations; periodic and almost periodic flows; asymptotically almost periodic solution
Summary:
Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the $l^p$-bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.
References:
[1] A. Halanay T. Morozan, C. Tudor: Bounded solutions of affine stochastic differential equations and stability. Časopis pro pěstování matematiky 111 (1986), 127-136. MR 0847312
[2] A. Halanay T. Morozan, C. Tudor: Tracking almost periodic signals white noise perturbations. Stochastics 21 (1987), 287-301. DOI 10.1080/17442508708833461 | MR 0905050
[3] A. Haraux: A simple almost-periodicity criterion and applications. J. Differential Equations 66 (1987), 51-61. DOI 10.1016/0022-0396(87)90039-8 | MR 0871570 | Zbl 0608.34049
[4] N. Ikeda, S. Watanabe: Stochastic Differential Equations and Diffusion Processes. North Holland, 1981. MR 1011252 | Zbl 0495.60005
[5] R. Khasminskii: Stability of Differential Equations under Random Perturbations. Nauka, 1969. (In russian.)
[6] Y. Miyahara: Ultimate boundedness of the systems governed by stochastic differential equations. Nagoya Math. J. 47 (1972), 111-144. DOI 10.1017/S0027763000014951 | MR 0319269 | Zbl 0222.60036
[7] T. Morozan: Bounded and periodic solutions of affine stochastic differential equations. Studii si Cercetari Matematice 38 (1986), 523-527. MR 0878757 | Zbl 0623.60075
[8] W. Römisch, A. Wakolbinger: On convergence rates of approximate solutions of stochastic equations. Lect. Notes in Control and Information Sciences 96, Springer-Verlag, 1986.
[9] A. Skorokhod: Studies in the Theory of Random Processes. Addison-Wesley, 1965. MR 0185620 | Zbl 0146.37701
[10] D. V. Stroock, S. R. Varadhan: Multidimensional Diffusion Processes. Springer-Verlag, 1979. MR 0532498 | Zbl 0426.60069
[11] C. Tudor: On Volterra equations driven by semimartingales. J. Differential Equations 72 no. 2 (1988), 200-217. DOI 10.1016/0022-0396(88)90002-2 | MR 0952895 | Zbl 0649.60072
[12] C. Vârsan: Asymptotic almost periodic solutions for stochastic differential equations. Tôhoku Math. J. 41 no. 4 (1989), 609-618. DOI 10.2748/tmj/1178227731 | MR 1025326
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