Conjectures on tail asymptotics of the marginal stationary distribution for a multidimensional SRBM

Authors:
Masakiyo Miyazawa;Masahiro Kobayashi
Affiliations:
Tokyo University of Science, Noda, Japan 278-8510;Tokyo University of Science, Noda, Japan 278-8510
Venue:
Queueing Systems: Theory and Applications
Year:
2011

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Abstract

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.