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Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations.
- Source :
-
Advances in Computational Mathematics . Aug2024, Vol. 50 Issue 4, p1-32. 32p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10197168
- Volume :
- 50
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Advances in Computational Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 178472749
- Full Text :
- https://doi.org/10.1007/s10444-024-10169-w