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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019028300
Forthcoming Article

Adjoint Forward Backward Stochastic Differential Equations Driven by Jump Diffusion Processes and Its Application to Nonlinear Filtering Problems

Feng Bao
Florida State University
yanzhao cao
Auburn University
Hongmei Chi
Florida A&M University

ABSTRACT

Forward backward stochastic differential equations (FBSDEs) were first introduced as a probabilistic interpretation for the Kolmogorov backward equation, and the solution of FBSDEs is equivalent to the solution of quasi-linear partial differential equations. In this work, we introduce the adjoint relation between a generalized FBSDE system driven by jump diffusion processes and its time inverse adjoint FBSDE system under the probabilistic framework without translating them into their corresponding PDEs. The ``exact solution" of a nonlinear filtering problem is derived as an application.