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Convergence rate of numerical solutions to SFDEs with jumps

Bao, Jianhai and Bottcher, Bjorn and Mao, Xuerong and Yuan, Chenggui (2011) Convergence rate of numerical solutions to SFDEs with jumps. Journal of Computational and Applied Mathematics, 236 (2). pp. 119-131. ISSN 0377-0427

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    Abstract

    In this paper, we are interested in numerical solutions of stochastic functional differential equations with jumps. Under a global Lipschitz condition, we show that the pth-moment convergence of Euler–Maruyama numerical solutions to stochastic functional differential equations with jumps has order 1/p for any p ≥ 2. This is significantly different from the case of stochastic functional differential equations without jumps, where the order is 1/2 for any p ≥ 2. It is therefore best to use the mean-square convergence for stochastic functional differential equations with jumps. Moreover, under a local Lipschitz condition, we reveal that the order of mean-square convergence is close to 1/2, provided that local Lipschitz constants, valid on balls of radius j, do not grow faster than log j.

    Item type: Article
    ID code: 36920
    Keywords: Euler-Maruyama, local Lipschitz condition, SFDE, convergence rate, Poisson process, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Faculty of Science > Mathematics and Statistics
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    Depositing user: Pure Administrator
    Date Deposited: 20 Jan 2012 15:16
    Last modified: 27 Mar 2014 21:14
    URI: http://strathprints.strath.ac.uk/id/eprint/36920

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