SHARP PATHWISE ASYMPTOTIC STABILITY CRITERIA FOR PLANAR SYSTEMS OF LINEAR STOCHASTIC DIFFERENCE EQUATIONS

abstract

• We consider the a.s. asymptotic stability of the equilibrium solution of a system of two linear stochastic difference equations with a parameter h > 0. These equations can be viewed as the Euler-Maruyama discretisation of a particular system of stochastic differential equations. However we only require that the tails of the distributions of the perturbing random variables decay quicker than certain polynomials. We use a version of the discrete It formula, and martingale convergence techniques, to derive sharp conditions on the system parameters for global a.s. asymptotic stability and instability when h is small.

authors

• Berkolaiko, Gregory

published proceedings

• DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

author list (cited authors)

• Berkolaiko, G., Kelly, C., & Rodkina, A.

complete list of authors

• Berkolaiko, Gregory||Kelly, Conall||Rodkina, Alexandra

publication date

• September 2011

published in

• Discrete and Continuous Dynamical Systems Series A  Journal

keywords

• A.s Asymptotic Stability
• Ito Formula
• Stochastic Difference Equations

start page

• 163

end page

• 173

issue

• SUPPL.