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Exact sampling of diffusions with a discontinuity in the drift. (English) Zbl 1426.65010

Summary: We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws related to those of Brownian motion and its local time, and are based on the principle of retrospective rejection sampling. A simple illustration is provided.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
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References:

[1] Beskos, A. and Roberts, G. (2005).Exact simulation of diffusions.Ann. Appl. Prob.15,2422-2444. · Zbl 1101.60060
[2] Beskos, A.,Papaspiliopoulos, O. and Roberts, G. O. (2006).Retrospective exact simulation of diffusion sample paths with applications.Bernoulli12,1077-1098. · Zbl 1129.60073
[3] Beskos, A.,Papaspiliopoulos, O. and Roberts, G. O. (2008).A factorisation of diffusion measure and finite sample path constructions.Methodology Comput. Appl. Prob.10,85-104. · Zbl 1152.65013
[4] Borodin, A. N. and Salminen, P. (2002).Handbook of Brownian Motion-Facts and Formulae,2nd edn.Birkhäuser,Basel. · Zbl 1012.60003
[5] Étoré, P. and Martinez, M. (2014).Exact simulation for solutions of one-dimensional stochastic differential equations with discontinuous drift.ESAIM Prob. Statist.18,686-702. · Zbl 1315.65008
[6] Taylor, K. B. (2015).Exact algorithms for simulation of diffusions with discontinuous drift and robust curvature Metropolis-adjusted Langevin algorithms. Doctoral Thesis, University of Warwick.
[7] Zvonkin, A. K. (1974).A transformation of the phase space of a diffusion process that removes the drift.Mat. Sb., Nov. Ser.93,129-149 (in Russian). English translation: Math. USSR-Sbornik22,129-149. · Zbl 0306.60049
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