| Biography | |
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 Prof. Remi Leandre University of Bourgogne-Franche-Comte, France |
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| Title: Bismut’s way of the Malliavin Calculus in the non Markovian case: an introduction. | |
| Abstract: This talk does a review on our last works on stochastic analysis where there is no stochastic process besides. It is devided in the following parts: -)In the first part, we perform Malliavin Calculus when there is a formal stochastic differential equation besides and establish by this way the existence of an heat kernel for fourth order generator. Malliavin matrix plays a key role. -)In part II, we establish Malliavin Calculus for big order generator when there is no formal stochastic differential equation besides and by using deeply the symmetry of the considered differential operator of big order, we show the existence of an heat kernel. No Malliavin matrix appears. -)In part III, we give a Bourbaki style meaning of part II, by considering a general class of rightinvariant elliptic pseudodifferential operator on a compact Lie group. -)In part IV, we perform the perturbation of a general elliptic pseudodifferential operator by a fractional power of it in order to establish the full relationship beteween Malliavin Calculus and the theory of pseudodifferential operator. -)In part V, we perform large deviation estimates for non Markovian semigroup, which enters in the theory of W.K.B. estimates but with different type of limit theorem. -)In part VI, we do the marriage of part V and the previous parts (according the beautifull requirement of Bismut’s book ”Large deviation and the Malliavin Calculus”) in order to establish some logarithmic estimates of the considered heat kernels in small time. A lot of of these results are classical in analysis but the method is new. | |
| Biography: Remi Leandre is directeur de recherches CNRS at the University of Bourgogne-Franche-Comte and works on the two sides of in nite dimensional analysis (Malliavin Calculus, White noise analysis) and their applications to geometry, analysis and mathematical physics.He has written about 170 papers in journals or conference proceedings about these topics. He received Bronze Medal of CNRS in 1988 and Rollo Davidson Prize in 1989 for various works on subelliptic heat-kernels. He is an editor with X. Dai, X. Ma and W. Zhang of two volumes "From probability to geometry: volume in honour of the 60th birthday of Jean-Michel Bismut" in Asterisque (Societe Mathematique de France) in 2009. | |
