摘要: We shall use the Euler-Maruyama (EM) scheme with decreasing step size $\Lambda=(\eta_n)_{n\in \mathbb{N}}$ to approximate the steady state for piecewise $\alpha$-stable Ornstein-Uhlenbeck processes arising in queue networks. These processes do not have an explicit dissipation. We prove the EM scheme converges to the steady state with a rate $\eta^{1/\alpha}_n$ in Wasserstein-1 distance. In addition, we utilize the Sinkhorn--Knopp algorithm to compute the Wasserstein-1 distance and conduct the simulations for several examples. This talk is based on a recent work together with Pang Guodong, Xu Lihu and Wang Y。

报告人简介：靳兴胡，合肥工业大学数学学院讲师。2021年博士毕业于澳门大学，主要研究方向：排队论系统稳态分布的逼近和随机微分方程遍历测度的逼近等，科研成果发表在Mathematics of Operations Research，Journal of Theoretical Probability 和 Potential Analysis等期刊上。