Almost sure convergence and asymptotic stability of systems of linear stochastic difference equations in ℝ d driven by L 2-martingales

Abstract

This paper presents a proof of almost sure asymptotic stability of trivial solution of stochastic systems of linear difference equations driven by -integrable martingale-type noise. For this purpose, we exploit a convergence theorem for non-negative semi-martingale decompositions and verify a practical criteria based on non-random eigenvalues. Two 2D examples illustrate the applicability of obtained criteria.