科研成果详情

In this paper we are concerned with distribution dependent backward stochastic differential equations (DDBSDEs) driven by Gaussian processes. We first show the existence and uniqueness of solutions to this type of equations. This is done by formulating a transfer principle to transfer the well-posedness problem to an auxiliary DDBSDE driven by Brownian motion. Then, we derive a comparison theorem under Lipschitz condition and boundedness of Lions derivative imposed on the generator. Furthermore, we get a new representation for DDBSDEs driven by Gaussian processes, this representation is even new for the case of the equations driven by Brownian motion. The newly obtained representation enables us to establish a converse comparison theorem, a novel contribution of the present paper. Finally, we prove transportation inequalities and Logarithmic-Sobolev inequalities via the stability of the Wasserstein distance and the relative entropy of measures under the homeomorphism condition.