Moment attractivity, stability and contractivity exponents of stochastic dynamical systems

Nonlinear stochastic dynamical systems as ordinary stochastic differential equations and stochastic difference equations are in the center of this pre sentation in view of the asymptotic behavior of their moments. We study the exponential p-th mean growth behavior of their solutions as integration ti me tends to infinity. For this purpose, the concepts of attractivity, stabi lity and contractivity exponents for moments are introduced as generalizati ons of well-known moment Lyapunov exponents of linear systems. Under approp riate monotonicity assumptions we gain uniform estimates of these exponents from above and below. Eventually, these concepts are generalized to descri be the exponential growth behavior along certain Lyapunov-type functionals.