Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment, and stability

Research output: Contribution to journalArticle

Solving stochastic differential equations (SDEs) numerically, explicit Euler-Maruyama (EM) schemes are used most frequently under global Lipschitz conditions for both drift and diffusion coefficients. In contrast, without imposing the global Lipschitz conditions, implicit schemes are often used for SDEs but require additional computational effort; along another line, tamed EM schemes and truncated EM schemes have been developed recently. Taking advantages of being explicit and easily implementable, truncated EM schemes are proposed in this paper. Convergence of the numerical algorithms is studied, and pth moment boundedness is obtained. Furthermore, asymptotic properties of the numerical solutions such as the exponential stability in pth moment and stability in distribution are examined. Several examples are given to illustrate our findings.
Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalIMA Journal of Numerical Analysis
StateAccepted/In press - 12 Feb 2018

    Research areas

  • local Lipschitz condition, explicit EM scheme, finite horizon, infinite horizon, pth moment convergence, moment bound, stability, invariant measure

Bibliographical note

This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Li, X, Mao, X & Yin, G 2018, 'Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment, and stability' IMA Journal of Numerical Analysis, pp. 1-36. is available online at: https://academic.oup.com/imajna

Projects

(1)
  1. Epsrc Doctoral Training Grant | Liang, Yanfeng

    Project: Research Studentship - Internally AllocatedResearch Studentship (Internally Allocated)

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