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BIT Numerical Mathematics

, Volume 48, Issue 1, pp 51–59 | Cite as

A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient

  • Nikolaos Halidias
  • Peter E. Kloeden
Article

Abstract

It is shown that the Euler–Maruyama scheme applied to a stochastic differential equation with a discontinuous monotone drift coefficient, such as a Heaviside function, and additive noise converges strongly to a solution of the stochastic differential equation with the same initial condition. The proof uses upper and lower solutions of the stochastic differential equations and the Euler–Maruyama scheme.

Key words

discontinuous monotone drift Euler–Maruyama scheme upper and lower solutions 

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Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Statistics and Actuarial-Finance MathematicsUniversity of the AegeanKarlovassiGreece
  2. 2.Institut für MathematikJohann Wolfgang Goethe UniversitätFrankfurt am MainGermany

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