Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T15:02:33.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact Simulation for Diffusion Bridges: An Adaptive Approach

Part of: Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  19 February 2016

Hongsheng Dai
Hongsheng Dai*
Affiliation:
University of Brighton
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Exact simulation approaches for a class of diffusion bridges have recently been proposed based on rejection sampling techniques. The existing rejection sampling methods may not be practical owing to small acceptance probabilities. In this paper we propose an adaptive approach that improves the existing methods significantly under certain scenarios. The idea of the new method is based on a layered process, which can be simulated from a layered Brownian motion with reweighted layer probabilities. We will show that the new exact simulation method is more efficient than existing methods theoretically and via simulation.

Keywords

Adaptive rejection samplingconditioned Brownian motiondiffusion bridgeexact Monte Carlo simulation

MSC classification

Primary: 65C05: Monte Carlo methods 65C50: Other computational problems in probability
Secondary: 60J60: Diffusion processes
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 346 - 358
Copyright
© Applied Probability Trust 

References

Beskos, A. and Roberts, G. O. (2005). Exact simulation on diffusions. Ann. Appl. Prob. 15, 2422–2444.CrossRefGoogle Scholar
Beskos, A., Papaspiliopoulos, O. and Roberts, G. O. (2006). Retrospective exact simulation of diffusion sample paths with applications. Bernoulli 12, 1077–1098.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Beskos, A., Papaspiliopoulos, O., Roberts, G. O. and Fearnhead, P. (2006). Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processess. J. R. Statist. Soc. B 68, 333–382.CrossRefGoogle Scholar
Casella, B. and Roberts, G. O. (2008). Exact Monte Carlo simulation of killed diffusions. Adv. Appl. Prob. 40, 273–291.CrossRefGoogle Scholar
Celeux, G., Hurn, M. and Roberts, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions. J. Amer. Statist. Assoc. 95, 957–970.CrossRefGoogle Scholar
Karatzas, I. and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, New York.Google Scholar
Øksendal, B. (1995). Stochastic Differential Equations, 4th edn. Springer, Berlin.CrossRefGoogle Scholar
Potzelberger, K. and Wang, L. (2001). Boundary crossing probability for Brownian motion. J. Appl. Prob. 38, 152–164.CrossRefGoogle Scholar
Roberts, G. O. and Tweedie, R. L. (1996). Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2, 341–363.CrossRefGoogle Scholar
Ross, S. M. (2007). Introduction to Probability Models. Academic Press.Google Scholar
Schurz, H. (2007). Modeling, analysis and discretization of stochastic logistic equations. Internat. J. Numer. Anal. Modeling 4, 178–197.Google Scholar