Abstract
The main result of the article deals with weak compactness of weak solutions sets of forward-backward stochastic differential inclusions. The main result is preceded by existence theorem for considered forward-backward stochastic differential inclusions. More precisely, we shall prove that by given set-valued mappings there exists a system consisting of a complete probability space , an d-dimensional continuous stochastic process X, an -dimensional càdlàg process Y, and an m-dimensional Brownian motion B defined on the space satisfying considered forward-backward stochastic differential inclusion and that each -martingale is an -martingale.
Acknowledgments
I am deeply indebted to my collegues Mariusz Michta and Jerzy Motyl for valueble discussions improving the text.
Disclosure statement
No potential conflict of interest was reported by the author