Convergence rate of numerical solutions to SFDEs with jumps

Jianhai Bao, Bjorn Bottcher, Xuerong Mao, Chenggui Yuan

Research output: Contribution to journalArticle

22 Citations (Scopus)
129 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)119-131
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume236
Issue number2
DOIs
Publication statusPublished - 15 Aug 2011

Keywords

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

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