This article is cited in 10 papers

An approximate solution of the prediction problem for stochastic jump-diffusion systems

T. A. Averina^ab, K. A. Rybakov<sup>c

a</sup> 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.

UDC: 519.676

Received: 08.07.2015
Revised: 11.12.2015

DOI: 10.15372/SJNM20170101

 English version: Numerical Analysis and Applications, 2017, 10:1, 1–10

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