A1673
Title: Smoothness of directed chain stochastic differential equations and its applications
Authors: Tomoyuki Ichiba - University of California Santa Barbara (United States) [presenting]
Abstract: On a filtered probability space for the space of continuous functions, a system of stochastic equations shall be considered: directed chain stochastic differential equations for a pair of stochastic processes whose marginal distributions in the path space are identical and their joint distribution is uniquely determined by the system of equations with the distributional constraints. The smoothness of the solutions is discussed under some regular conditions first, and some relaxation of the conditions is then considered on the coefficients and the distributional constraints. Its applications are also introduced in such systems in the stochastic filtering problem and in the generative adversarial network problem.
