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Abstract |
The typical way to find the stationary distributions of stochastic differential equations is to solve the Kolmogorov-Fokker-Planck equations. However, in most cases this process is nontrivial and it is not easy to find the explicit expression of the stationary distributions. In this talk, I will discuss the approximation of the stationary distributions of the underlying equations by the numerical stationary distributions derived from the backward Euler-Maruyama method. Sufficient conditions on the drift and diffusion coefficients that guarantee the existence and uniqueness of the numerical stationary distributions are obtained first. Then, I will show that the numerical stationary distributions converge to the underlying stationary distributions as the time step vanishes. |
