A multi-dimensional SRBM: geometric views of its product form stationary distribution
نویسندگان
چکیده
منابع مشابه
A multi-dimensional SRBM: geometric views of its product form stationary distribution
We present a geometric interpretation of a product form stationary distribution for a d-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The d-dimensional SRBM data can be equivalently specified by d + 1 geometric objects: an ellipse and d rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing p...
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We present three sets of results for the stationary distribution of a two-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative quadrant. The SRBM data can equivalently be specified by three geometric objects, an ellipse and two lines, in the two-dimensional Euclidean space. First, we revisit the variational problem (VP) associated with the SRBM. Building on...
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This research has been inspired by several papers on processes with inert drift [5, 6, 4, 3, 1]. The model involves a “particle” X and an “inert drift” L, neither of which is a Markov process by itself, but the vector process (X, L) is Markov. It turns out that for a number of diffusions with inert drift, the stationary measure has the product form; see [1]. The purpose of this note is to chara...
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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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We consider a general model for continuous-time Markov chains representing queueing systems in random environment. First we study the relationship between its equilibrium distribution and the Palm (or embedded) distributions at certain environmental change epochs. The results enable one to obtain the equilibrium distribution of the continuous-time model in terms of the equilibrium distribution ...
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ژورنال
عنوان ژورنال: Queueing Systems
سال: 2014
ISSN: 0257-0130,1572-9443
DOI: 10.1007/s11134-014-9411-0