The Annals of Applied Probability

Exact simulation of diffusions

Alexandros Beskos and Gareth O. Roberts

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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.

Article information

Ann. Appl. Probab. Volume 15, Number 4 (2005), 2422-2444.

First available: 7 December 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65] 65C05: Monte Carlo methods

Exact simulation rejection sampling Girsanov theorem boundary hitting time


Beskos, Alexandros; Roberts, Gareth O. Exact simulation of diffusions. The Annals of Applied Probability 15 (2005), no. 4, 2422--2444. doi:10.1214/105051605000000485.

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