Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients

Xuerong Mao, Lukasz Szpruch

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Abstract

In this work, we generalize the current theory of strong convergence rates for the
backward Euler–Maruyama scheme for highly non-linear stochastic differential
equations, which appear in both mathematical finance and bio-mathematics. More
precisely, we show that under a dissipative condition on the drift coefficient and superlinear growth condition on the diffusion coefficient the BEM scheme converges with strong order of a half. This type of convergence gives theoretical foundations for efficient variance reduction techniques for Monte Carlo simulations. We support our theoretical results with relevant examples, such as stochastic population models and stochastic volatility models.
Original languageEnglish
Pages (from-to)144-171
Number of pages28
JournalStochastics: An International Journal of Probability and Stochastic Processes
Volume85
Issue number1
Early online date10 Feb 2012
DOIs
Publication statusPublished - 10 Feb 2013

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Keywords

  • stochastic differential equation
  • dissipative model
  • strong convergence
  • backward Euler–Maruyama method
  • dissipative-type
  • super-linear diffusion coefficients

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