Using Stein's Method to Analyze Euler-Maruyama Approximations of Regime-Switching Jump Diffusion Processes

作者：Jin, Xinghu; Shen, Tian; Su, Zhonggen^*

来源：Journal of Theoretical Probability, 2023, 36(3): 1797-1828.

DOI：10.1007/s10959-022-01221-w

• Euler-Maruyama scheme
• Jacobi flow
• Markovian switching
• Poisson process
• Stein's equation

For a kind of regime-switching jump diffusion process (X-t, Z(t))(t >= 0), under some conditions, it is exponentially ergodic under the weighted total variation distance with ergodic measure mu. We use the Euler-Maruyama scheme of the process (X-t, Z(t))(t >= 0) which has an ergodic measure mu(eta) (eta is the step size of the Euler-Maruyama scheme) to approximate the ergodic measure mu. Furthermore, we use Stein's method to prove that the convergence rate of mu(eta) to mu is eta(1/2) in terms of some function-class distance dG(mu, mu(eta)).

• 单位
  浙江大学