##### Department of Mathematics,

University of California San Diego

****************************

### Stochastic Systems Seminar

## Prof. Jim Dai

#### Cornell University

## Asymptotic product-form stationary distributions for reflected Brownian motions

##### Abstract:

We prove that a sequence of multi-scaled stationary distributions of reflected Brownian motions (RBMs) has a product-form limit. Each component in the limit is an exponential distribution. The multi-scaling corresponds to the "multi-scale heavy traffic" recently advanced in Dai, Glynn and Xu (2023) for generalized Jackson networks. The proof utilizes the basic adjoint relationship (BAR) first introduced in Harrison and Williams (1987) that characterizes the stationary distribution of an RBM. This is joint work with Jin Guang and Xinyun Chen at CUHK-Shenzhen, and Peter Glynn at Stanford.

### May 11, 2023

### 1:00 PM

Via Zoom (for Zoom information, please email Professor Williams)

****************************