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.
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Miyazawa, M., Kobayashi, M. Conjectures on tail asymptotics of the marginal stationary distribution for a multidimensional SRBM. Queueing Syst 68, 251–260 (2011). https://doi.org/10.1007/s11134-011-9251-0
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DOI: https://doi.org/10.1007/s11134-011-9251-0
Keywords
- Queueing network
- Semi-martingale reflecting Brownian motion
- Stationary distribution
- Tail asymptotic
- Tail decay rate
- Stationary inequality
- Multidimensional moment generating function