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Seminar on Stochastic Analysis, Random Fields and Applications V pp 57–74Cite as

Dirichlet Forms Methods: An Application to the Propagation of the Error Due to the Euler Scheme

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Part of the book series: Progress in Probability ((PRPR,volume 59))

Abstract

We present recent advances on Dirichlet forms methods either to extend financial models beyond the usual stochastic calculus or to study stochastic models with less classical tools. In this spirit, we interpret the asymptotic error on the solution of an sde due to the Euler scheme (Kurtz and Protter [39]) in terms of a Dirichlet form on the Wiener space, what allows to propagate this error thanks to functional calculus.

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Authors and Affiliations

  1. Ecole Nationale des Ponts et des Chaussées, 6 et 8 avenue Blaise Pascal Cité Descartes, Champs sur Marne, 77455, Marne-la-Vallée Cedex 2, France

    Nicolas Bouleau

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  1. Nicolas Bouleau
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Editors and Affiliations

  1. Institut de Mathématiques, Ecole Polytechnique Fédérale, CH-1005, Lausanne, Switzerland

    Robert C. Dalang

  2. Département de Mathématiques, Institut Galilée, Université Paris 13, F-95430, Villetaneuse, France

    Francesco Russo

  3. Institut Elie Cartan, Université Henri Poincaré, B.P. 239, F-54506, Vandoeuvre-lès-Nancy Cedex, France

    Marco Dozzi

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Bouleau, N. (2007). Dirichlet Forms Methods: An Application to the Propagation of the Error Due to the Euler Scheme. In: Dalang, R.C., Russo, F., Dozzi, M. (eds) Seminar on Stochastic Analysis, Random Fields and Applications V. Progress in Probability, vol 59. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8458-6_5

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