Approximation of the steady state for piecewise stable Ornstein-Uhlenbeck processes arising in queueing networks

This is the authors' abstract. We don't add key points for this paper.

We shall use the Euler-Maruyama (EM) scheme with decreasing step size Λ=(ηₙ)n∈ N to approximate the steady state for piecewise α-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 η1/αₙ 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.