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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 1, Pages 1–13
DOI: https://doi.org/10.15372/SJNM20170101 (Mi sjvm631) 		 
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
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DOI: https://doi.org/10.15372/SJNM20170101
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-5111.2014.1
Russian Foundation for Basic Research 13-08-00323-а
14-01-00787-а
Received: 08.07.2015
Revised: 11.12.2015
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 1, Pages 1–10
DOI: https://doi.org/10.1134/S1995423917010013
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
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