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Discrete Itô Formula for Delay Stochastic Difference Equations with Multiple Noises

  • Alexandra RodkinaEmail author
Conference paper
  • 896 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 94)

Abstract

For stochastic difference equation with multiple noises, finite delays and a parameter h we prove a variant of discrete Itô formula. Then we apply the formula to derive conditions which provide either P{lim n →  x n  = 0} = 1 or P{liminf n →   | x n  |  > 0} = 1, where x n is a solution of the equation with sufficiently small parameter h.

Keywords

Stochastic difference equation with multiple noises and finite delays Discrete Itô formula Asymptotic stability and instability Martingale convergence theorems 

Notes

Acknowledgements

The author thanks the anonymous referee for encouraging remarks and useful suggestions.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the West IndiesKingston 7Jamaica

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