L'aplicabilitat de la fórmula d'integració per parts en un espai gaussià

Authors

  • Eulàlia Nualart

Abstract

Integration by parts formula in a Gaussian space and its applications. In the 70?s, the french mathematician Paul Malliavin revolutionized the probability theory when he introduced the stochastic calculus of variations that today has his name. Malliavin constructed a differentiable structure in a Gaussian space such that the Itô integral was a differentiable object. His main motivation was to use this theory in order to provide a probabilistic proof of Hörmander?s theorem for second order hypoelliptic operators. One of the key tools of this differential stochastic calculus is its integration by parts formula that concerns two operators, the derivative and its adjoint, named the Skorohod integral. We will introduce the basic notions of the Malliavin calculus, and we will give some of its applications to three different -but very related- areas of mathematics, which are probability, statistics and mathematical finance.

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Published

2012-03-02

How to Cite

Nualart, E. (2012). L’aplicabilitat de la fórmula d’integració per parts en un espai gaussià. Butlletí De La Societat Catalana De Matemàtiques, 26(2), 137–163. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/73749.001

Issue

Vol. 26 No. 2 (2011)

Section

Articles

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