Nonlinear filtering of stochastic differential equations driven by correlated Lévy noises

2019/07/15 by Huijie Qiao, Qiao, Huijie
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.1907.06779

Abstract

The work concerns nonlinear filtering problems of stochastic differential equations with correlated Lévy noises. First, we establish the Kushner-Stratonovich and Zakai equations through martingale representation theorems and the Kallianpur-Striebel formula. Second, we show the pathwise uniqueness and uniqueness in joint law of weak solutions for the Zakai equation. Finally, we investigate the uniqueness in joint law of weak solutions to the Kushner-Stratonovich equation.

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