Uniqueness and superposition of the space-distribution dependent Zakai equations

2020/08/03 by Meiqi Liu, Huijie Qiao, Liu, Meiqi +1
Economics, Econometrics and Finance · #35K55 #60G35 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2008.01596

openalex publication_date 2020/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The work concerns the space-distribution dependent Zakai equations from nonlinear filtering problems of McKean-Vlasov stochastic differential equations with correlated noises. First of all, we establish the space-distribution dependent Kushner-Stratonovich equations and the space-distribution dependent Zakai equations. Then, the pathwise uniqueness of their strong solutions is shown. Finally, we prove a superposition principle between the space-distribution dependent Zakai equations and space-distribution dependent Fokker-Planck equations. As a by-product, we give some conditions under which space-distribution dependent Fokker-Planck equations have weak solutions.

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