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Contemporary Mathematics. Fundamental Directions, 2006, Volume 17, Pages 110–128
(Mi cmfd60)
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This article is cited in 9 scientific papers (total in 9 papers)
Almost sure polynomial asymptotic stability of stochastic difference equations
J. Applebya, D. Mackeyb, A. Rodkinac a 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.
Citation:
J. Appleby, D. Mackey, A. Rodkina, “Almost sure polynomial asymptotic stability of stochastic difference equations”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 3, CMFD, 17, PFUR, M., 2006, 110–128; Journal of Mathematical Sciences, 149:6 (2008), 1629–1647
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https://www.mathnet.ru/eng/cmfd60 https://www.mathnet.ru/eng/cmfd/v17/p110
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Abstract page: | 462 | Full-text PDF : | 149 | References: | 46 |
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