Exponential convergence to quasi-stationary distribution and \(Q\) -process

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• 作者：Nicolas Champagnat ; Denis Villemonais
• 关键词：Process with absorption ; Quasi ; stationary distribution ; $$Q$$ Q ; process ; Dobrushin’s ergodicity coefficient ; Uniform mixing property ; Birth and death process ; Neutron transport process ; Primary 60J25 ; 37A25 ; 60B10 ; 60F99 ; Secondary 60J80 ; 60G10 ; 92D25
• 刊名：Probability Theory and Related Fields
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：164
• 期：1-2
• 页码：243-283
• 全文大小：829 KB
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• 作者单位：Nicolas Champagnat (1) (2)
  Denis Villemonais (1) (2)
  
  1. Université de Lorraine, IECN, Campus Scientifique, B.P. 70239, Vandœuvre-lès-Nancy Cedex, 54506, France
  2. Inria, TOSCA Team, Villers-lès-Nancy, 54600, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the \(Q\)-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death processes with catastrophes, multi-dimensional birth and death processes, infinite-dimensional population models with Brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain. Keywords Process with absorption Quasi-stationary distribution \(Q\)-process Dobrushin’s ergodicity coefficient Uniform mixing property Birth and death process Neutron transport process