scholarly journals Existence and Uniqueness of Quasi-stationary Distributions for Symmetric Markov Processes with Tightness Property

2019 ◽  
Vol 32 (4) ◽  
pp. 2006-2019
Author(s):  
Masayoshi Takeda
Keyword(s):  
Markov Processes ◽  
Existence And Uniqueness ◽  
Stationary Distributions ◽  
Symmetric Markov Processes

Stationary distributions for piecewise-deterministic Markov processes

1990 ◽  
Vol 27 (1) ◽  
pp. 60-73 ◽  
Author(s):  
O. L. V. Costa
Keyword(s):  
Markov Chain ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Capacity Expansion ◽  
Stationary Distributions ◽  
Mild Conditions ◽  
Piecewise Deterministic Markov Processes

In this paper we show that the problem of existence and uniqueness of stationary distributions for piecewise-deterministic Markov processes (PDPs) is equivalent to the same problem for the associated Markov chain, so long as some mild conditions on the parameters of the PDP are satisfied. Our main result is the construction of an invertible mapping from the set of stationary distributions for the PDP to the set of stationary distributions for the Markov chain. Some sufficient conditions for existence are presented and an application to capacity expansion is given.

Stationary distributions for piecewise-deterministic Markov processes

1990 ◽  
Vol 27 (01) ◽  
pp. 60-73 ◽  
Author(s):  
O. L. V. Costa
Keyword(s):  
Markov Chain ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Capacity Expansion ◽  
Stationary Distributions ◽  
Mild Conditions ◽  
Piecewise Deterministic Markov Processes

In this paper we show that the problem of existence and uniqueness of stationary distributions for piecewise-deterministic Markov processes (PDPs) is equivalent to the same problem for the associated Markov chain, so long as some mild conditions on the parameters of the PDP are satisfied. Our main result is the construction of an invertible mapping from the set of stationary distributions for the PDP to the set of stationary distributions for the Markov chain. Some sufficient conditions for existence are presented and an application to capacity expansion is given.

scholarly journals On invariant measures of nonlinear Markov processes

1993 ◽  
Vol 6 (4) ◽  
pp. 385-406 ◽  
Author(s):  
N. U. Ahmed ◽  
Xinhong Ding
Keyword(s):  
Markov Process ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Nonlinear Markov Processes

We consider a nonlinear (in the sense of McKean) Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.

Flux and Lateral Conditions for Symmetric Markov Processes

2008 ◽  
Vol 29 (3) ◽  
pp. 241-269
Author(s):  
Zhen-Qing Chen ◽  
Masatoshi Fukushima
Keyword(s):  
Markov Processes ◽  
Symmetric Markov Processes
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