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Exact simulation of one-dimensional stochastic differential equations involving the local time at zero of the unknown process. (English) Zbl 1269.65007
Authors’ abstract: We extend the exact simulation methods of A. Beskos, O. Papaspiliopoulos and G. O. Roberts [Bernoulli 12, No. 6, 1077–1098 (2006; Zbl 1129.60073)] to the solutions of one-dimensional stochastic differential equations (SDEs) involving the local time of the unknown process at point zero. In order to perform the method, we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case where the solution of the SDE with local time corresponds to a divergence form operator with a discontinuous coefficient at zero. Numerical examples are shown to illustrate the method and the performances are compared with more traditional discretization schemes.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60J65 Brownian motion
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