2-microlocal analysis of martingales and stochastic integrals

Abstract : Recently, a new approach in the fine analysis of stochastic processes sample paths has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved that the almost sure 2-microlocal frontier of a martingale can be obtained through the local regularity of its quadratic variation. It allows to link the Hölder regularity of a stochastic integral to the regularity of the integrand and integrator processes. These results provide a methodology to predict the local regularity of diffusions from the fine analysis of its coefficients. We illustrate our work with examples of martingales with unusual complex regularity behavior and square of Bessel processes.
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Stochastic Processes and their Applications, Elsevier, 2012, 122, pp.2346-2382. 〈10.1016/j.spa.2012.03.011〉
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https://hal-ecp.archives-ouvertes.fr/hal-00734418
Contributeur : Erick Herbin <>
Soumis le : vendredi 21 septembre 2012 - 17:19:37
Dernière modification le : jeudi 5 avril 2018 - 12:30:21

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Paul Balança, Erick Herbin. 2-microlocal analysis of martingales and stochastic integrals. Stochastic Processes and their Applications, Elsevier, 2012, 122, pp.2346-2382. 〈10.1016/j.spa.2012.03.011〉. 〈hal-00734418〉

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