Dirichlet Forms in Simulation

Bouleau Nicolas ()
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Bouleau Nicolas: bouleau@enpc.fr

Monte Carlo Methods and Applications, 2005, vol. 11, issue 4, 385-395

Abstract: Equipping the probability space with a local Dirichlet form with square field operator Γ and generator A allows to improve Monte Carlo computations of expectations, densities, and conditional expectations, as soon as we are able to simulate a random variable X together with Γ[X] and A[X]. We give examples on the Wiener space, on the Poisson space and on the Monte Carlo space. When X is real-valued we give an explicit formula yielding the density at the speed of the law of large numbers.

Keywords: square field operator; Wiener space; Poisson space; density; stochastic differential equation; Dirichlet form; error (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1515/156939605777438541

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