Système de processus auto-stabilisants
Samuel Herrmann
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Taking an odd increasing Lipschitz-continuous function with polynomial growth β, an odd Lipschitz-continuous and bounded function ϕ satisfying sgn(x)ϕ(x) ≥ 0 and a parameter a ∈ [1/2,1], we consider the (nonlinear) stochastic differential system ⎧, (E)⎨ ⎩, and , where , and are independent Brownian motions. We show that (E) admits a stationary probability measure, and, under some additional conditions, that converges in distribution to this invariant measure. Moreover we...