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International Journal of Differential Equations
Volume 2011 (2011), Article ID 575383, 26 pages
http://dx.doi.org/10.1155/2011/575383
Research Article

Malliavin Calculus of Bismut Type for Fractional Powers of Laplacians in Semi-Group Theory

Institut de Mathématiques, Université de Bourgogne, 21000 Dijon, France

Received 2 March 2011; Revised 16 May 2011; Accepted 2 June 2011

Academic Editor: Nikolai Leonenko

Copyright © 2011 Rémi Léandre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We translate into the language of semi-group theory Bismut's Calculus on boundary processes (Bismut (1983), Lèandre (1989)) which gives regularity result on the heat kernel associated with fractional powers of degenerated Laplacian. We translate into the language of semi-group theory the marriage of Bismut (1983) between the Malliavin Calculus of Bismut type on the underlying diffusion process and the Malliavin Calculus of Bismut type on the subordinator which is a jump process.