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Uniform exponential dichotomy of stochastic cocycles. (English) Zbl 1201.60060
Summary: The aim of this paper is to give a generalization of the well-known theorem of O.Perron [M. Z. 32, 703–728 (1930; JFM 56.1040.01)] for uniform exponential dichotomy in mean square for stochastic cocycles in Hilbert spaces.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
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[1] Arnold, L., Stochastic differential equations: theory and applications, (1972), Wiley New York
[2] L. Arnold, Random Dynamical Systems, Springer Monographs in Mathematics, Berlin, 1998. · Zbl 0906.34001
[3] Ateiwi, A.M., About bounded solutions of linear stochastic ito systems, Miskolc math. notes, 3, 1, 3-12, (2002)
[4] Bensoussan, A.; Flandoli, F., Stochastic inertial manifold, Stoch. stoch. rep., 53, 1-2, 13-39, (1995) · Zbl 0854.60059
[5] Buse, C.; Barbu, D., The Lyapunov equations and nonuniform exponential stability, Stud. cerc. mat., 49, 1-2, 25-31, (1997) · Zbl 0893.93031
[6] Chow, S.N.; Leiva, H., Two definitions of exponential dichotomy for skew-product semiflow in Banach spaces, Proc. amer. math. soc., 124, 1071-1081, (1996) · Zbl 0845.34064
[7] Da Prato, G.; Zabczyc, J., Stochastic equations in infinite dimensions, (1992), University Press Cambridge
[8] Flandoli, F., Stochastic flows for non-linear second-order parabolic SPDE, Ann. probab., 24, 2, 547-558, (1996) · Zbl 0870.60056
[9] Megan, M.; Sasu, A.L.; Sasu, B., On uniform exponential stability of linear skew-product semiflows in Banach spaces, Bull. belg. math. soc. Simon stevin, 9, 143-154, (2002) · Zbl 1032.34046
[10] Mohammed, S.E.A.; Zhang, T.; Zhao, H., (), 98
[11] Perron, O., Die stabilitatsfrage bei differentialgeighungen, Math. Z., 32, 703-728, (1930) · JFM 56.1040.01
[12] Preda, P., On a Perron condition for evolutionary process in Banach spaces, Bull. math. soc. sci. math. R.S. roumanie, 32(80), 1, 65-70, (1988) · Zbl 0649.34066
[13] Preda, P.; Megan, M., Nonuniform dichotomy of evolutionary processes in Banach spaces, Bull. aust. math. soc., 27, 31-52, (1983) · Zbl 0503.34030
[14] Skorohod, A.V., Random linear operators, (1984), Riedel
[15] D. Stoica, Exponential stability and exponential instability for stochastic cocycle, in: Proceedings of the XII-th Symposium of Mathematics and its Applications, Timişoara, 2009, pp. 182-187. · Zbl 1212.60106
[16] Stoica, D., Exponential stability for stochastic cocycle, Annals of the tiberiu Popoviciu seminar of functional equations, Approximation and convexity, cluj-napoca, 7, 111-118, (2009) · Zbl 1181.60090
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