Almost sure polynomial asymptotic stability of stochastic difference equations |
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Authors: | J. A. D. Appleby D. Mackey A. Rodkina |
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Affiliation: | (1) School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland;(2) School of Mathematical Sciences, Dublin Institute of Technology, Dublin 8, Ireland;(3) Department of Mathematics and Computer Science, The University of the West Indies, Mona, Kingston 7, Jamaica |
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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 that 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. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 17, Differential and Functional Differential Equations. Part 3, 2006. |
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