Exact simulation of diffusions
Alexandros Beskos and Gareth O. Roberts
Source: Ann. Appl. Probab. Volume 15, Number 4
(2005), 2422-2444.
Abstract
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random collection of time instances. The path can then be completed without further reference to the dynamics of the target process.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1133965767
Digital Object Identifier: doi:10.1214/105051605000000485
Mathematical Reviews number (MathSciNet): MR2187299
Zentralblatt MATH identifier: 05039564
References
Devroye, L. (1986). Nonuniform Random Variate Generation. Springer, New York.
Mathematical Reviews (MathSciNet): MR836973
Forsythe, G. E. (1972). von Neumann's comparison method for random sampling from the normal and other distributions. Math. Comp. 26 817--826.
Mathematical Reviews (MathSciNet): MR315863
Karatzas, I. and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus, 2nd ed. Springer, New York.
Mathematical Reviews (MathSciNet): MR1121940
Zentralblatt MATH: 0734.60060
Kendall, W. S. (1997). On some weighted Boolean models. In Advances in Theory and Applications of Random Sets (D. Jeulin, ed.) 105--120. World Scientific, Singapore.
Mathematical Reviews (MathSciNet): MR1654418
Kloeden, P. E. and Platen, E. (1995). Numerical Solution of Stochastic Differential Equations. Springer, Berlin.
Lerche, H. R. (1986). Boundary Crossing of Brownian Motion. Springer, Berlin.
Mathematical Reviews (MathSciNet): MR861122
Zentralblatt MATH: 0604.62075
McKean, H. P. (1969). Stochastic Integrals. Academic Press, New York.
Mathematical Reviews (MathSciNet): MR247684
Zentralblatt MATH: 0191.46603
Oksendal, B. K. (1998). Stochastic Differential Equations\up: An Introduction with Applications. Springer, Berlin.
Mathematical Reviews (MathSciNet): MR1619188
Papaspiliopoulos, O. and Roberts, G. O. (2005). Retrospective MCMC methods for Dirichlet process hierarchical models. Unpublished manuscript.
The Annals of Applied Probability
