An Introduction to Backward Stochastic Differential Equations and Their Applications
speaker: Rainer Buckdahn (Université de Bretagne Occidentale (Brest), Laboratoire de Mathématiques CNRS-UMR 6205)abstract: The aim of this mini-lecture is to give an introduction into the theory of backward stochastic differential equations (in short, BSDEs), a theory which has known a quick and very dynamic development since the first paper on non linear BSDEs, written by Pardoux and Peng in 1992, a development which has been motivated by the vast field of applications, in particular in finance, stochastic control and deterministic and stochastic partial differential equations.
In a first section, after giving some motivation, the lecture will focus on two different notions of existence, existence of a solution in the strong sense, i.e., on a given filtered probability space, and existence in the weak sense, i.e. existence of an appropriate filtered probability space on which a solution can be constructed. Both notions of existence and the corresponding notions of uniqueness, the pathwise uniqueness and uniqueness in law, will be studied.
After this general discussion of BSDEs, a second section will be devoted to the study of BSDEs in a Markovian framework and its connections with viscosity solutions of second order PDEs and Stochastic PDEs. In the third section some applications of the theory of BSDEs will be discussed. In this discussion the attention will be focused to problems of homogenization for PDEs.
Backward SPDE (studied by Jin Ma and others)
timetable:
Tue 24 May, 10:40 - 12:30, Aula Dini
Wed 25 May, 14:30 - 15:10, Aula Dini
Wed 25 May, 15:20 - 16:00, Aula Dini
Thu 26 May, 10:40 - 12:30, Aula Dini
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