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Plenary Lecture
Applications of the Malliavin Calculus of Bismut type without probability
Remi Leandre
Institut de Mathematiques. Universite de Bourgogne
21000. Dijon. FRANCE
Remi.leandre@u-bourgogne.fr
Abstract: This talk is divided in 4 parts:
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In the first part,
we translate the Malliavin Calculus of Bismut type in semi-group theory.
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In the second part,
we translate in semi-group theory the proof of Varadhan estimates, lower bound,
for subelliptic diffusions we got a lot of time ago by using the probability
theory.
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In the third part,
we translate in semi-group theory the proof of the positivity theorem we got a
lot time ago with Ben Arous by using the Bismutian procedure. We translate in
particular in semi-group theory the Wong-Zakai approximation of a diffusion in
stochastic analysis.
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In the fourth part,
we translate in semi-group theory some pathological results for hypoelliptic
diffusion we got a lot of time ago by using an adaptation in probability of the
Rothschild-Stein inhomogeneous division method.
Brief Biography of the Speaker:
1957: Born in Belfort (France).
1978/1981: Student Ecole Normale Superieure Saint-Cloud.
1980: Agregation de Mathematiques. Rank: 5.
1982/1984: National service at the University of Monastir (Tunisia).
1984: These de Troisieme cycle. Directeur: J.M. Bismut.
1984/1988: assistant at the Universite de Besancon.
1987: Habilitation a diriger les recherches. Universite de Besancon. Directeur:
J.M. Bismut.
1988: Bronze medal of C.N.R.S.
1988/1994: Charge de recherches Premiere classe C.N.R.S. Universite de
Strasbourg.
1989: Rollo Davidson Price.
1994/2004: Directeur de recherches Seconde Classe. C.N.R.S. Universite de Nancy.
2003: Editor of a special issue ”Probability and geometry” of the Journal
”Infinite dimensional analysis, quantum probability and related topics”.
2004: Directeur de recherches Seconde Classe. Universite de Dijon.
Organiser of various conferences:
- ”Loops spaces” (Strasbourg 1994)with S. Paycha and T. Wuerzbacher.
- ”Probability and geometry” (Nancy 1999).
- ”Infinite dimensional analysis” (C.I.R.M. 2001).
- I have organized a session ”Analysis on path spaces” at the Satellite
Conference of Stochastic Analysis of I.C.M. at Beijing (2002).
- ”Infinite dimensional analysis and path integrals” (C.I.R.M 2004) with C.
De Witt-Morette.
- ”Stochastic analysis and mathematical physics” (Dijon. 2006).
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