Lihu Xu

activity

20242026

collaborators

6 papers

math.PR2026

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 $R^{2 d}$ : \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…

math.PR2025

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 $η_{1} \geq η_{2} \geq \dots$ are decreasing, and prove that the EM scheme weakly converge…

math.PR2024

$W_{d}$ -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 $I^^{3}$ -order HÃ¶lder and dissipative conditions on the coefficients, we derive the $W_{d}$ -con…

math.PR2024

Unbiased approximation of the ergodic measure for piecewise $I^\pm$ -stable Ornstein-Uhlenbeck processes arising in queueing networks

Xinghu Jin, Guodong Pang, Yu Wang +1

Piecewise $I^\pm$ -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…

math.ST2024

Robust estimation for high-dimensional time series with heavy tails

Yu Wang, Guodong Li, Zhijie Xiao +2

We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $I^\pm$ -th moment with $I^\pm \in (1, 2]$ . T…

stat.ML2024

Error estimates between SGD with momentum and underdamped Langevin diffusion

Arnaud Guillin, Yu Wang, Lihu Xu +1

Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped La…