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Extra Form
Lecturer Michael Roeckner
Dept. Bielefeld Univ./Purdue Univ.
date Oct 20, 2011
Fokker-Planck and Kolmogorov (backward) equations can be interpreted as linearisations of the underlying stochastic differential equations (SDE). It turns out that, in particular, on infinite dimensional spaces (i.e. for example if the SDE is a stochastic partial differential equation (SPDE) of evolutionary type), the Fokker-Planck equation is much better to analyze than the Kolmogorov (backward) equation. The reason is that the Fokker-Planck equation is a PDE for measures. Hence e.g. existence of solutions via compactness arguments is easier to show than for PDE on functions. On the other hand uniqueness appears to be much harder to prove.
In this talk we first give a quite elaborate introduction into the relations between S(P)DE, Fokker-Planck and Kolmogorov equations. Subsequently, we shall sketch a new method to prove uniqueness of solutions for Fokker-Planck equations.
Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
Math Colloquia Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
Math Colloquia Convex and non-convex optimization methods in image processing file Hong Kong Baptist University Michael Ng
Math Colloquia A new view of Fokker-Planck equations in finite and Infinite dimensional spaces file Bielefeld Univ./Purdue Univ. Michael Roeckner
Math Colloquia Unprojection file University of Warwick / 서강대 Miles Reid
Math Colloquia Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
Math Colloquia Connes's Embedding Conjecture and its equivalent file RIMS Narutaka Ozawa
Math Colloquia Recent progress on the Brascamp-Lieb inequality and applications file Saitama University Neal Bez
Math Colloquia Unique ergodicity for foliations file Université Paris-Sud Nessim Sibony
Math Colloquia Idempotents and topologies file University of Waterloo Nico Spronk
Math Colloquia Contact Homology and Constructions of Contact Manifolds file 서울대 Otto van Koert
Math Colloquia <학부생을 위한 ɛ 강연> Symplectic geometry and the three-body problem file 서울대학교 Otto van Koert
Math Colloquia Q-curvature in conformal geometry file 서강대 Pak Tung Ho
Math Colloquia Symmetry Breaking in Quasi-1D Coulomb Systems file 서강대학교 Paul Jung
Math Colloquia It all started with Moser file Univ. of Wisconsin/포항공대 Paul Rabinowitz
Math Colloquia Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
Math Colloquia Fefferman's program and Green functions in conformal geometry file 서울대학교 Raphaël Ponge
Math Colloquia Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients file University of Illinois Renming Song
Math Colloquia Green’s function for initial-boundary value problem file National Univ. of Singapore Shih-Hsien Yu
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