Distribution dependent BSDEs driven by Gaussian processes

2023/02/07 by Xiliang Fan, Fan, Xiliang, Jiang-Lun Wu +1
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2302.03412

openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 establish 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 new obtained representation enables us to prove a converse comparison theorem. Finally, we derive transportation inequalities and Logarithmic-Sobolev inequalities via the stability of the Wasserstein distance and the relative entropy of measures under the homeomorphism condition.

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