On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations

Abstract

The multiplicative ergodic theorem is valid under an integrability condition on the linearized flow with respect to an invariant measure. We investigate the case were the flow is generated by . . . a s:ochas:ic diKeien:ia! ecjna:ion and give a criterion in t e r m ~f !he :' ecto: fie!& ar,d the (generally non-adapted) invariant measure assuring the validity of the integrability condition.

Random Dynamical Systems

“…We have, however, the following quite satisfactory general criterion (see Arnold and Imkeller[22]). We have, however, the following quite satisfactory general criterion (see Arnold and Imkeller[22]).…”

Dynamics of random transformations: smooth ergodic theory

“…V] for statements and a brief review. An interesting phenomenon in that case, proved by Baxendale [23] and Kifer [87], is that all the integrability conditions required on the C r -norms hold true automatically (see Arnold and Imkeller [8] for further results in this direction).…”

On the Spatial Asymptotic Behavior of Stochastic Flows in Euclidean Space

“…This function was first introduced in [4] to obtain moduli of continuity for the local time of one-dimensional diffusions in the spatial parameter and used in [2] for establishing conditions under which the multiplicative ergodic theorem holds. The significance of the functions c is that solutions of SDE's with Lipschitz coefficients have finite c -moments for some (but usually not all) c > 0.…”