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International Journal for Uncertainty Quantification
Fator do impacto: 4.911 FI de cinco anos: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Imprimir: 2152-5080
ISSN On-line: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019028300
pages 143-159

ADJOINT FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY JUMP DIFFUSION PROCESSES AND ITS APPLICATION TO NONLINEAR FILTERING PROBLEMS

Feng Bao
Department of Mathematics, Florida State University, Tallahassee, Florida 32306, USA
Yanzhao Cao
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849; School of Mathematics, Sun Yat Sun University, China
Hongmei Chi
Department of Computer and Information Sciences, Florida A&M University, Tallahassee, Florida 32306, USA

RESUMO

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 quasilinear 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.

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