Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations (in EN)
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.
- Research Organization:
- Auburn Univ., AL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0022253
- OSTI ID:
- 2576228
- Journal Information:
- Advances in Computational Mathematics, Journal Name: Advances in Computational Mathematics Journal Issue: 4 Vol. 50; ISSN 1019-7168
- Publisher:
- SpringerCopyright Statement
- Country of Publication:
- United States
- Language:
- EN
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