Abstract
In this paper we introduce decompositions of diffusion measure which are used to construct an algorithm for the exact simulation of diffusion sample paths and of diffusion hitting times of smooth boundaries. We consider general classes of scalar time-inhomogeneous diffusions and certain classes of multivariate diffusions. The methodology presented in this paper is based on a novel construction of the Brownian bridge with known range for its extrema, which is of interest on its own right.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Asmussen, P. Glynn, and J. Pitman, “Discretization error in simulation of one-dimensional reflecting Brownian motion,” Annals of Applied Probability vol. 5 pp. 875–896, 1995.
J. Bertoin, and J. Pitman, “Path transformations connecting Brownian bridge, excursion and meander,” Bulletin des Sciences Mathématiques vol. 118 pp. 147–166, 1994.
A. Beskos, O. Papaspiliopoulos, and G. O. Roberts, “Retrospective exact simulation of diffusion sample paths with applications,” Bernoulli vol. 12 pp. 1077–1098, 2006.
A. Beskos, and G. O. Roberts, “Exact simulation of diffusions,” Annals of Applied Probability vol. 15 pp. 2422–2444, 2005.
J. L. Doob, “Heuristic approach to the Kolmogorov-Smirnov theorems,” Annals of Mathematical Statistics vol. 20 pp. 393–403, 1949.
J. F. C. Kingman, Poisson processes, vol. 3 of Oxford Studies in Probability, The Clarendon Press Oxford University Press, Oxford Science Publications: New York, 1993. Oxford Science Publications, 1993.
P. E. Kloeden, and E. Platen, Numerical Solution of Stochastic Differential Equations, vol. 23 of Applications of Mathematics (New York). Springer-Verlag: Berlin, 1992.
K. Pötzelberger, and L. Wang, “Boundary crossing probability for Brownian motion,” Journal of Applied Probability vol. 38 pp. 152–164, 2001.
L. A. Shepp, “The joint density of the maximum and its location for a Wiener process with drift.” Journal of Applied Probability vol. 16 pp. 423–427, 1979.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beskos, A., Papaspiliopoulos, O. & Roberts, G.O. A Factorisation of Diffusion Measure and Finite Sample Path Constructions. Methodol Comput Appl Probab 10, 85–104 (2008). https://doi.org/10.1007/s11009-007-9060-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11009-007-9060-4