- Date: 20 Nov. (Fri.)
- Place: On the Web (and Tokyo Satellite Campus of Ritsumeikan University; If you would like to come to the campus, please contact us by email: ritsumeikanmathfiseminar@gmail.com )
- Time: 19:00 – 20:00
- Speaker: Tadashi Hayashi (Mitsubishi UFJ trust and banking)
- Title: The existence and uniqueness of a solution to Double Barrier Backward Doubly Stochastic Differential Equations
- Abstract:

Double barrier backward doubly stochastic differential equations (DB-BDSDEs, for short) are equations with two different directions of stochastic integrals, i.e., the equations involve both a standard “forward” stochastic integral and a “backward” stochastic integral with two mutually independent standard Brownian motions, and with two reflection barriers. This kind of equations is a joint version of backward doubly stochastic differential equations (BDSDEs, for short) and double barrier backward stochastic differential equations (DB-BSDEs, for short). The former has been introduced by Pardoux and Peng. They ave proved the connection with a class of systems of quasilinear SPDEs and the existence and uniqueness result of such PDEs. The latter has been tackled by Hamadene et al. In this talk, we try to show the outline of the proof for the existence and uniqueness of a solution to DB-BDSDEs by using the “penalization method”, so-called under appropriate conditions. At the end of this talk, we introduce our next some studies that we are tackling now.