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This article is cited in 10 scientific papers (total in 10 papers)
An approximate solution of the prediction problem for stochastic jump-diffusion systems
T. A. Averinaab, K. A. Rybakovc a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva, 6, Novosibirsk, 630090, Russia
b Novosibirsk State University, Pirogova str., 2, Novosibirsk, 630090, Russia
c Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoye sh., 4, A-80, GSP-3, Moscow, 125993, Russia
Abstract:
In this paper we discuss the evolution of the new approach to the prediction problem for nonlinear stochastic differential systems with a Poisson component. The proposed approach is based on reducing the prediction problem to the analysis of stochastic jump-diffusion systems with terminating and branching paths. The solution of the prediction problem can be approximately found by using numerical methods for solving stochastic differential equations and methods for modeling inhomogeneous Poisson flows.
Key words:
branching processes, conditional density, Duncan–Mortensen–Zakai equation, Kolmogorov–Feller equation, Monte Carlo method, optimal filtering problem, prediction problem, stochastic jump-diffusion system.
Received: 08.07.2015 Revised: 11.12.2015
Citation:
T. A. Averina, K. A. Rybakov, “An approximate solution of the prediction problem for stochastic jump-diffusion systems”, Sib. Zh. Vychisl. Mat., 20:1 (2017), 1–13; Num. Anal. Appl., 10:1 (2017), 1–10
Linking options:
https://www.mathnet.ru/eng/sjvm631 https://www.mathnet.ru/eng/sjvm/v20/i1/p1
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Abstract page: | 1945 | Full-text PDF : | 48 | References: | 27 | First page: | 6 |
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