Conjectures on tail asymptotics of the marginal stationary distribution for a multidimensional SRBM
We are concerned with the stationary distribution of a d-dimensional semimartingale reflecting Brownian motion on a nonnegative orthant, provided it is stable, and conjecture about the tail decay rate of its marginal distribution in an arbitrary direction. Due to recent studies, the conjecture is true for d=2. We show its validity for the skew symmetric case for a general d.
tail asymptotic stationary distribution tail decay rate queueing network semi-martingale reflecting brownian motion stationary inequality multidimensional moment generating function