Alternative fluid approximation approach for the steady-state distribution of the two-sided reflected Markov modulated Brownian motion and its computation

The steady-state distribution of the two-sided reflected Markov Modulated Brownian motion is derived through an alternative fluid approximation approach. In this paper, we have shown that the distribution can be obtained by taking limit on the steady-state distribution of a weakly convergent Markov...

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Bibliographic Details
Published in:Journal of the Korean Statistical Society Vol. 44; no. 3; pp. 448 - 456
Main Author: Ahn, Soohan
Format: Journal Article
Language:English
Published: Singapore Elsevier B.V 01.09.2015
Springer Singapore
한국통계학회
Subjects:
Applied Statistics
Bayesian Inference
Duality
Markov modulated Brownian motion
Quadratically convergent algorithm
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Steady-state distribution
Weak convergence
통계학
secondary
Weak convergence
Quadratically convergent algorithm
Steady-state distribution
Markov modulated Brownian motion
Duality
primary
primary 60K25
secondary 90B05
ISSN:1226-3192, 2005-2863
Online Access:Get full text
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Summary:The steady-state distribution of the two-sided reflected Markov Modulated Brownian motion is derived through an alternative fluid approximation approach. In this paper, we have shown that the distribution can be obtained by taking limit on the steady-state distribution of a weakly convergent Markov modulated fluid model. In addition, we present how the duality theorem developed by Ahn and Ramaswami is applied to get the limit result. For computation, we introduce a quadratically convergent algorithm and its related theories which rely on the fluid approximation approach. Through numerical examples, we finally illustrate behaviors of the steady-state distribution and also some performances of the algorithm.
Bibliography:G704-000337.2015.44.3.011
ISSN:1226-3192
2005-2863
DOI:10.1016/j.jkss.2014.12.005