Modern Stochastics: Theory and Applications

A solution is given to generalized backward stochastic differential equations driven by a real-valued RCLL martingale on an arbitrary filtered probability space. The existence and uniqueness of a solution are proved via the Yosida approximation method when the generators are only stochastic monotone with respect to the y-variable and stochastic Lipschitz with respect to the z-variable, with different linear growth conditions.

This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.