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A Note on Euler Approximations for Stochastic Differential Equations with Delay

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Abstract

An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.

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  1. Maxwell Institute for Mathematical Sciences and School of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, UK

    Istvan Gyöngy & Sotirios Sabanis

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  1. Istvan Gyöngy
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  2. Sotirios Sabanis
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Correspondence to Sotirios Sabanis.

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Gyöngy, I., Sabanis, S. A Note on Euler Approximations for Stochastic Differential Equations with Delay. Appl Math Optim 68, 391–412 (2013). https://doi.org/10.1007/s00245-013-9211-7

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  • DOI: https://doi.org/10.1007/s00245-013-9211-7

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