## Moment contractivity and stability exponents of nonlinear stochastic dynamical systems

• Nonlinear stochastic dynamical systems as ordinary stochastic differential equations and stochastic difference methods are in the center of this presentation in view of the asymptotical behaviour of their moments. We study the exponential p-th mean growth behaviour of their solutions as integration time tends to infinity. For this purpose, the concepts of nonlinear contractivity and stability exponents for moments are introduced as generalizations of well-known moment Lyapunov exponents of linear systems. Under appropriate monotonicity assumptions we gain uniform estimates of these exponents from above and below. Eventually, these concepts are generalized to describe the exponential growth behaviour along certain Lyapunov-type functionals.

Author: Henri Schurz urn:nbn:de:hbz:386-kluedo-7667 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (215) Preprint English 1999 1999 Technische Universität Kaiserslautern 1999/11/30 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Fxx Equations and systems with randomness [See also 34K50, 60H10, 93E03] / 34F05 Equations and systems with randomness [See also 34K50, 60H10, 93E03] 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05] 93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp; lp, etc.) Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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