This article is cited in 10 papers

Almost sure polynomial asymptotic stability of stochastic difference equations

J. Appleby^a, D. Mackey^b, A. Rodkina<sup>c

a</sup> Dublin City University
^b Dublin Institute of Technology
^c University of the West Indies

Abstract: In this paper, we establish the almost sure asymptotic stability and decay results for solutions of an autonomous scalar difference equation with a nonhyperbolic equilibrium at the origin, which is perturbed by a random term with a fading state–independent intensity. In particular, we show that if the unbounded noise has tails which fade more quickly than polynomially, then the state–independent perturbation dies away at a sufficiently fast polynomial rate in time, and if the autonomous difference equation has a polynomial nonlinearity at the origin, then the almost sure polynomial rate of decay of solutions can be determined exactly.

UDC: 517.55+517.95

 English version: Journal of Mathematical Sciences, 2008, 149:6, 1629–1647

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