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Almost sure exponential stability of numerical solutions for stochastic delay differential equations

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Abstract

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Fuke Wu

  2. Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK

    Xuerong Mao & Lukas Szpruch

Authors
  1. Fuke Wu
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  2. Xuerong Mao
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  3. Lukas Szpruch
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Correspondence to Fuke Wu.

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Wu, F., Mao, X. & Szpruch, L. Almost sure exponential stability of numerical solutions for stochastic delay differential equations. Numer. Math. 115, 681–697 (2010). https://doi.org/10.1007/s00211-010-0294-7

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  • DOI: https://doi.org/10.1007/s00211-010-0294-7

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