An approximate solution of the prediction problem for stochastic jump-diffusion systems
T.A. Averina1,2, K.A. Rybakov3
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
2Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia
3Moscow Aviation Institute, Volokolamskoye sh. 4, A-80, GSP-3, Moscow, 125993, Russia
Keywords: апостериорная плотность вероятности, ветвящиеся процессы, метод статистических испытаний, оптимальная фильтрация, прогнозирование, стохастическая система, уравнение Дункана-Мортенсена-Закаи, уравнение Колмогорова-Феллера, branching processes, conditional density, Duncan-Mortensen-Zakai equation, Kolmogorov-Feller equation, Monte Carlo method, optimal filtering problem, prediction problem, stochastic jump-diffusion system
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.
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