Statistical filtering algorithms based on the maximum cross section method for stochastic systems with regime switching

Abstract

New statistical algorithms are formed to estimate the state vector of stochastic systems with regime switching. These algorithms are based on the particle method, i.e., on numerical methods for solving stochastic differential equations, methods for modeling conditional Markov processes with a finite set of states, and methods for calculating weights. An important part of proposed algorithms is the use of the maximum cross section method and its modification, which allows the exact simulation of the regime switching process. This paper continues the authors’ research in the field of statistical methods and algorithms of the analysis and filtering for continuous-time stochastic systems.