Cameron–Martin Type Theorem for a Class of non-Gaussian Measures

da Silva José, University of Madeira

In this presentation, we show the quasi-invariance property of a class of non-Gaussian measures, known as Mittag-Leffler measures. In other words, we prove a Cameron-Martin type theorem to the generalized grey Brownian motion introduced by Schneider, Mainardi and co-authors; see [3], [2,1]. These measures are a mixture of Gaussian measures and the related processes are subordinated Gaussian processes, namely subordinated fractional Brownian motion. This feature enables us to find the Cameron-Martin type theorem expressed in terms of the stochastic integral with respect to fractional Brownian motion. As a consequence, we obtain an integration by parts and the closability of the gradient operator. The results of the presentation are based on the joint work with M. Erraoui and M. Röckner.


[1] A. Mura and F. Mainardi. A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics. Integr. Transf. Spec. F., 20(2009):185–198.

[2] A. Mura and G. Pagnini. Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A: Math. Theor., 41(2008):285003, 22.

[3] W. R. Schneider. Grey noise. In S. Albeverio, G. Casati, U. Cattaneo, D. Merlini, and R. Moresi, editors, Stochastic Processes, Physics and Geometry, 676–681. World Scientific Publishing, Teaneck, NJ, 1990.

Area: CS39 - Fractional operators and anomalous diffusions (Luisa Beghin)

Keywords: Cameron-Martin theorem, fractional Brownian motion, subordination

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