Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations

Evelyn Buckwar, Cónall Kelly

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

We develop two classes of test equations for th e linear stability analysis of numerical methods applied to systems of stochastic ordinary differential equations of Itô type (SODEs). Motivated by the theory of stochastic stabilization and destabilization, these test equations capture certain fundamental effects of stochastic perturbation in systems of SODEs, while remaining amenable to analysis before and after discretization. We then carry out a linear stability analysis of the ?-Maruyama method applied to these test equations, investigating mean-square and almost sure asymptotic stability of the test equilibria. We discuss the implications of our work for the notion of A-stability of the ?-Maruyama method and use numerical simulation to suggest extensions of our results to test systems with nonnormal drift coefficients. © 2010 Society for Industrial and Applied Mathematics.

Original languageEnglish
Pages (from-to)298-321
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number1
DOIs
Publication statusPublished - 2010

Keywords

  • Destabilization
  • Linear stability analysis
  • Stabilization
  • Systems of stochastic differential equations
  • Theta method

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