We give a short introduction to Malliavin calculus which finishes with the proof The Malliavin derivative and the Skorohod integral in the finite. Application du calcul de Malliavin aux problèmes de contrôle singulier. Devant le jury. Abdelhakim Necir. Pr. UMK Biskra Président. Brahim Mezerdi. Pr. Using multiple Wiener%It/o stochastic integrals and Malliavin calculus we servant des int egrales multiples de Wiener%It/o et du calcul de Malliavin, nous.

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Stochastic calculus Integral calculus Mathematical finance Calculus of variations. In particular, it allows the computation of derivatives of random variables. This page was last edited on 12 Octoberat Retrieved from ” https: This article includes a list of referencesrelated reading or external linksbut its sources remain unclear because malllavin lacks inline citations.


The calculus has been applied to stochastic partial differential equations. A similar idea can be mlaliavin in stochastic analysis for the differentiation along a Cameron-Martin-Girsanov direction.

Application du calcul de Malliavin aux équations différentielles stochastiques sur le plan

In probability theory and related fields, Malliavin calculus is a amlliavin of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. Views Read Edit View history. Malliavin calculus is also called the stochastic calculus of variations. June Learn how and when to remove this template message.

From Wikipedia, the free encyclopedia. A simplified version of this theorem is as follows:.

The existence of this adjoint follows from the Riesz representation theorem for linear operators on Hilbert spaces. The calculus has applications callcul, for example, stochastic filtering.

Malliavin calculus – Wikipedia

The calculus allows integration by parts with random variables ; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. All articles with unsourced statements Articles with unsourced statements from August Articles lacking in-text malliabin from June All articles lacking in-text citations. His calculus enabled Malliavin to prove regularity bounds for the solution’s density.


One of the most useful results from Malliavin calculus is the Clark-Ocone theoremwhich allows the process in the martingale representation theorem to be identified explicitly. By using this site, you agree to the Terms of Use and Privacy Policy. The calculus has applications for example in stochastic filtering. The calculus has been applied to stochastic partial differential equations as well.