Abstract
In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by Lévy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a superposition principle, a limit theorem of stochastic differential equations driven by Lévy processes. Then we apply the result to a type of nonlinear filtering problems and obtain the convergence of the nonlinear filterings.
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Acknowledgements
The author is very grateful to Professor Renming Song for valuable discussions. Moreover, the author also would like to thank the anonymous referee for giving useful suggestions to improve this paper.
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This work was partly supported by NSF of China (Nos. 11001051, 11371352, 12071071) and China Scholarship Council under Grant No. 201906095034.
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Qiao, H. Limit theorems of SDEs driven by Lévy processes and application to nonlinear filtering problems. Nonlinear Differ. Equ. Appl. 29, 8 (2022). https://doi.org/10.1007/s00030-021-00741-4
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DOI: https://doi.org/10.1007/s00030-021-00741-4
Keywords
- Lévy processes
- Non-local Fokker–Planck equations
- Superposition principles
- Nonlinear filtering problems
- The robustness