NONLINEAR SELF-STABILIZING PROCESSES - II - CONVERGENCE TO INVARIANT PROBABILITY

We now analyze the asymptotic behaviour of X-t, as t approaches infini ty, X being solution of X-t = X-0 + B-t - 1/2 integral(0)(t) b(s,X-s)d s b(s, x) = E[beta(x - X-s)], (1) where beta is a given odd and increa sing Lipschitz-continuous function with polynomial growth. We prove wi th additional assumptions on beta that X-t converges in distribution t o the invariant probability measure associated with Eq. (1). (C) 1998 Published by Elsevier Science B.V. All rights reserved.