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Exact simulation of multidimensional reflected Brownian motion

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

Published online by Cambridge University Press:  28 March 2018

Jose Blanchet  and
Karthyek Murthy
Jose Blanchet*
Affiliation:
Columbia University
Karthyek Murthy*
Affiliation:
Columbia University
*
* Current address: Management Science and Engineering, Stanford University, 475 Via Ortega, Stanford, CA 94305, USA. Email address: [email protected]
** Postal address: Department of Industrial Engineering & Operations Research, Columbia University, S. W. Mudd Building, 500 W. 120 Street, New York, NY 10027, USA.
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Abstract

We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called ε-strong simulation techniques (also known as tolerance-enforced simulation) which allow us to provide a piecewise linear approximation to RBM with ε (deterministic) error in uniform norm. A novel conditional acceptance–rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied.

Keywords

Unbiased samplingrefine until accept/rejecttolerance enforced simulationacceptance–rejection samplingε-strong simulationiterative algorithmintersection layer

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60J60: Diffusion processes 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 137 - 156
Copyright
Copyright © Applied Probability Trust 2018 

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