Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient

Gunther Leobacher, Michaela Szölgyenyi

Publication: Scientific journalJournal articlepeer-review

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Abstract

We prove strong convergence of order 1/4−ϵ for arbitrarily small ϵ>0 of the Euler–Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler–Maruyama scheme and another numerical method, which is constructed by applying the Euler–Maruyama scheme to a transformation of the SDE we aim to solve.
Original languageEnglish
Pages (from-to)219 - 239
JournalNumerische Mathematik
Volume138
Issue number1
DOIs
Publication statusPublished - 2018

Austrian Classification of Fields of Science and Technology (ÖFOS)

  • 101014 Numerical mathematics
  • 401117 Viticulture
  • 101024 Probability theory
  • 101007 Financial mathematics

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