×

Exact simulation for solutions of one-dimensional stochastic differential equations with discontinuous drift. (English) Zbl 1315.65008

This paper proposes an exact simulation algorithm for the solution of a scalar unit additive system of stochastic differential equations in which the deterministic function is smooth apart from a discontinuity at \(0\). The approach is based on considering the convergence of a series of solutions to a skew perturbed additive noise problem in which the solutions converge to a limit algorithm of an exact simulation algorithm and extending it to the problem considered here. The exact simulation algorithm is based on building a skeleton with appropriate rejection procedure. Some simple simulations illustrate the approach.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
65L20 Stability and convergence of numerical methods for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI arXiv