Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching

This work focuses on numerical algorithms for approximating the ergodic means for suitable functions of solutions to stochastic differential equations with Markov regime switching. Our main effort is devoted to obtaining the convergence and rates of convergence of the approximation algorithms. The study is carried out by obtaining laws of large numbers and laws of iterated logarithms for numerical approximation to long-run averages of suitable functions of solutions to switching diffusions.