5 papers · 1 filter
Long term convergence rate of Smoluchowski-Kramers approximation by Stein's method
Shiyu Liu, Wei Liu, Lihu Xu
We consider the following second-order stochastic differential equation on : \begin{equation*} dX_t^m=Y_t^mdt, \quad mdY_t^m=b(X_t^m)dt+Ï(X_t^m)dB_t-Y^m_tdt, \end…
Functional central limit theorem for Euler--Maruyama scheme with decreasing step sizes
Qiyang Pei, Lihu Xu
We consider the Euler--Maruyama (EM) scheme of a family of dissipative SDEs, whose step sizes are decreasing, and prove that the EM scheme weakly converge…
-convergence rate of EM schemes for invariant measures of supercritical stable SDEs
Peng Chen, Lihu Xu, Xiaolong Zhang +1
By establishing the regularity estimates for nonlocal Stein/Poisson equations under -order Hölder and dissipative conditions on the coefficients, we derive the -con…
Unbiased approximation of the ergodic measure for piecewise -stable Ornstein-Uhlenbeck processes arising in queueing networks
Xinghu Jin, Guodong Pang, Yu Wang +1
Piecewise -stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Eul…
Quantitative diffusion approximation for the Neutral -Alleles Wright-Fisher Model with Mutations
Peng Chen, Jie Xiong, Lihu Xu +1
We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral -alleles using a diffusion process, deriving an error rate ba…