In this work, we study the exponential stability of stationary distribution a McKean-Vlasov equation, nonlinear hyperbolic type which was recently derived in [1], [2]. We complement convergence result proved [2] using tools from dynamical systems theory. Our proof relies on two principal arguments addition to Picard-like iteration method. First, linearized semigroup is positive allows precisely...

Abstract. A class of implicit methods is introduced for Ito stochastic differential equations with Poisson-driven jumps. A convergence proof shows that these implicit methods share the same strong finite-time convergence rate as the explicit Euler–Maruyama scheme. A mean-square linear stability analysis shows that implicitness offers benefits, and a natural analogue of mean-square A-stability i...

1. Introduction. The problem we address here arises in the study of the error function in the shifted circle problem (see [BCDL]). Let α = (α 1 , α 2) ∈ R

We associate with a stochastic cocycle Θ = (φ,Φ), on Y = Ω×H, a stochastic variational integral equation and we characterize the exponential instability in mean square of stochastic equations in therms of solvability of the associated equation. Thus we obtain a generalization of stochastic case for results obtained by O. Perron [8], in deterministic case. 2000Mathematics Subject Classification:...

Abstract This article investigates the mean‐square strong stability and stabilization of a discrete‐time stochastic system corrupted by multiplicative noises. First, definition (MS) is addressed to avoid overshoots in dynamics, two necessary sufficient conditions for MS‐strong are derived. Moreover, relationship between MS‐stability given. Second, some via state feedback (SF) output obtained, r...