Retrospective exact simulation of diffusion sample paths with applications

Bernoulli

Volumn 12, Issue 6, 2006, Pages 1077-1098

  Beskos, Alexandros ^a   Papaspiliopoulos, Omiros ^a   Roberts, Gareth O ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Conditioned diffusion processes; Discretely observed diffusions; Exact simulation; Monte Carlo maximum likelihood; Rejection sampling

Indexed keywords

EID: 35349014465     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1165269151     Document Type: Article

References (19)

1. Asmussen, S., Glynn, P. and Pitman, J. (1995) Discretization error in simulation of one-dimensional reflecting Brownian motion. Ann. Appl. Probab., 5(4), 875-896.
2. Bertoin, J. and Pitman, J. (1994) Path transformations connecting Brownian bridge, excursion and meander. Bull. Sci. Math., 118(2), 147-166.
3. Beskos, A.P. and Roberts, G.O. (2005) Exact simulation of diffusions. Ann. Appl. Probab., 15, 2422-2444.
4. Borodin, A.N. and Salminen, P. (2002) Handbook of Brownian motion-Facts and Formulae, 2nd edn. Basel: Birkhauser.
5. Chib, S., Pitt, M.K. and Shephard, N. (2004) Likelihood-based inference for diffusion driven models. Unpublished manuscript. http://www.nuff.ox.ac.uk/economics/papers/2004/w20/chibpittshephard.pdf.
6. Devroye, L. (1986) Nonuniform Random Variate Generation. New York: Springer-Verlag.
7. Gelfand, A.E. and Smith, A.F.M. (1990) Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc., 85, 398-409.
8. Goel, N.S. and Richter-Dyn, N. (1974) Stochastic Models in Biology. New York: Academic Press.
9. Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus, 2nd edn. New York: Springer-Verlag.
10. Karlin, S. and Taylor, H.M. (1981) A Second Course in Stochastic Processes. New York: Academic Press.
11. Kloeden, P.E. and Platen, E. (1995) Numerical Solution of Stochastic Differential Equations. Berlin: Springer-Verlag.
12. Oksendal, B.K. (1998) Stochastic Differential Equations: An Introduction with Applications. Berlin: Springer-Verlag.
13. Papaspiliopoulos, O. and Roberts, G.O. (2004) Retrospective MCMC methods for Dirichlet process hierarchical models. Manuscript. Department of Mathematics and Statistics, Lancaster University. Submitted for publication. http://www.maths.lancs.ac.uk/∼papaspil/research.html. In revision.
14. Propp, J. and Wilson, D. (1998) Coupling from the past: a user’s guide. In Microsurveys in Discrete Probability (Princeton, NJ 1997), volume 41 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pp. 181-192. Providence, RI: American Mathematical Society.
15. Revuz, D. and Yor, M. (1991) Continuous Martingales and Brownian Motion. Berlin: Springer-Verlag.
16. Roberts, G.O. and Stramer, O. (2001) On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm. Biometrika, 88(3), 603-621.
17. Rogers, L.C.G. and Williams, D. (2000) Diffusions, Markov Processes, and Martingales. Vol. 2: Ito Calculus. Cambridge: Cambridge University Press.
18. Sorensen, H. (2004) Parametric inference for diffusion processes observed at discrete points in time: a survey. Internat. Statist. Rev., 72, 337-354.
19. Stuart, A.M., Voss, J. and Wiberg, P. (2004) Conditional path sampling of SDEs and the Langevin MCMC method. Comm. Math. Sci., 2, 685-697