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Dirichlet Forms in Simulation

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  • Bouleau Nicolas

    (bouleau@enpc.fr)

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.

Suggested Citation

  • Bouleau Nicolas, 2005. "Dirichlet Forms in Simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 11(4), pages 385-395, December.
    • Handle: RePEc:bpj:mcmeap:v:11:y:2005:i:4:p:385-395:n:3
    DOI: 10.1515/156939605777438541
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/1802 is not listed on IDEAS
    2. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
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