| 个人简介 | |
|---|---|
 Prof. Remi Leandre University of Bourgogne-Franche-Comte, France |
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| 标题： Bismut’s way of the Malliavin Calculus in the non Markovian case: an introduction. | |
| 摘要：
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.
| |
| 简介：
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.
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