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Exact sampling of diffusions with a discontinuity in the drift

  • Omiros Papaspiliopoulos (a1), Gareth O. Roberts (a2) and Kasia B. Taylor (a2)

Abstract

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.

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Corresponding author

Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25‒27, 08005 Barcelona, Spain. Email address: omiros.papaspiliopoulos@upf.edu
Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK. Email address: gareth.o.roberts@warwick.ac.uk
Department of Statistics and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. Email address: kasia.taylor@warwick.ac.uk

References

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[1] Beskos, A. and Roberts, G. (2005).Exact simulation of diffusions.Ann. Appl. Prob. 15,24222444.
[2] Beskos, A.,Papaspiliopoulos, O. and Roberts, G. O. (2006).Retrospective exact simulation of diffusion sample paths with applications.Bernoulli 12,10771098.
[3] Beskos, A.,Papaspiliopoulos, O. and Roberts, G. O. (2008).A factorisation of diffusion measure and finite sample path constructions.Methodology Comput. Appl. Prob. 10,85104.
[4] Borodin, A. N. and Salminen, P. (2002).Handbook of Brownian Motion–Facts and Formulae,2nd edn.Birkhäuser,Basel.
[5] Étoré, P. and Martinez, M. (2014).Exact simulation for solutions of one-dimensional stochastic differential equations with discontinuous drift.ESAIM Prob. Statist. 18,686702.
[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. 93,129149 (in Russian). English translation: Math. USSR–Sbornik 22,129149.

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Exact sampling of diffusions with a discontinuity in the drift

  • Omiros Papaspiliopoulos (a1), Gareth O. Roberts (a2) and Kasia B. Taylor (a2)

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