In principle, once the existence of the stationary distribution of a stochastic differential equation with Markovian switching is assured, we may compute it by solving the associated system of the coupled Kolmogorov-Fokker-Planck equations. However, this is nontrivial in practice. As a viable alternative, we use the Euler-Maruyama scheme to obtain the stationary distribution in this paper.
- Brownian motion
- stationary distribution
- Lipschitz condition
- Markov chain
- stochastic differential equations
- Euler-Maruyama methods
- weak convergence to stationary measures