TY - JOUR

T1 - Solving approximately a prediction problem for stochastic jump-diffusion systems

AU - Averina, T. A.

AU - Rybakov, K. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, a new approach to solving a prediction problem for nonlinear stochastic differential systems with a Poisson component is discussed. In this approach, the prediction problem is reduced to an analysis of stochastic jump-diffusion systems with terminating and branching paths. The prediction problem can be approximately solved by using numerical methods for stochastic differential equations and methods for modeling inhomogeneous Poisson flows.

AB - In this paper, a new approach to solving a prediction problem for nonlinear stochastic differential systems with a Poisson component is discussed. In this approach, the prediction problem is reduced to an analysis of stochastic jump-diffusion systems with terminating and branching paths. The prediction problem can be approximately solved by using numerical methods for stochastic differential equations and methods for modeling inhomogeneous Poisson flows.

KW - branching processes

KW - conditional density

KW - Duncan–Mortensen–Zakai equation

KW - Kolmogorov–Feller equation

KW - Monte Carlo method

KW - optimal filtering problem

KW - prediction problem

KW - stochastic jump-diffusion system

KW - Duncan-Mortensen-Zakai equation

KW - Kolmogorov-Feller equation

UR - http://www.scopus.com/inward/record.url?scp=85014759672&partnerID=8YFLogxK

U2 - 10.1134/S1995423917010013

DO - 10.1134/S1995423917010013

M3 - Article

AN - SCOPUS:85014759672

VL - 10

SP - 1

EP - 10

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -