On stochastic regression models with continuous time

Abstract

Two processes described by related impulse dynamical systems are considered. When combined, they are an analogue of the autoregressive model with GARCH errors and Markov process instead of "white noise" as well as with switching moments, which are random, that is, with Poisson’s flow. In the analysis of the behavior of these processes, modeling of the solutions of impulse dynamic systems in MATLAB, averaging of the initial systems, diffusive approximation of normalized deviations of the initial processes from the solutions of the corresponding averaged equations and modeling of the solutions for the obtained diffusion equations with the program MATHEMATICA are combined.