The obstacle problem for quasilinear stochastic integral-partial differential equations. Issue 2 (17th February 2020) - Dong, Yuchao
ABSTRACT: We prove the existence and uniqueness of solutions to a kind of quasilinear stochastic integral-partial differential equations with obstacles. Our method is based on the probabilistic interpretation of the solutions so that penalization method can be applied to a sequence of backward doubly stochastic differential equations with jumps. Relations between regular potentials and regular measures play an important role.