Convergence rate of numerical solutions to SFDEs with jumps

Jianhai Bao, Bjorn Bottcher, Xuerong Mao, Chenggui Yuan

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.
LanguageEnglish
Pages119-131
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume236
Issue number2
DOIs
Publication statusPublished - 15 Aug 2011

Fingerprint

Stochastic Functional Differential Equations
Jump
Rate of Convergence
Differential equations
Numerical Solution
Mean-square Convergence
Lipschitz condition
Lipschitz
Euler
Ball
Radius
Valid
Moment

Keywords

  • Euler-Maruyama
  • local Lipschitz condition
  • SFDE
  • convergence rate
  • Poisson process

Cite this

Bao, Jianhai ; Bottcher, Bjorn ; Mao, Xuerong ; Yuan, Chenggui. / Convergence rate of numerical solutions to SFDEs with jumps. In: Journal of Computational and Applied Mathematics. 2011 ; Vol. 236, No. 2. pp. 119-131.
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Convergence rate of numerical solutions to SFDEs with jumps. / Bao, Jianhai; Bottcher, Bjorn; Mao, Xuerong; Yuan, Chenggui.

In: Journal of Computational and Applied Mathematics, Vol. 236, No. 2, 15.08.2011, p. 119-131.

Research output: Contribution to journalArticle

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