Exponential ergodicity of general Markov processes

1979 ◽  
Vol 11 (02) ◽  
pp. 279-280
Author(s):  
Pekka Tuominen ◽  
Richard L. Tweedie
Keyword(s):  
Markov Processes ◽  
Exponential Ergodicity

scholarly journals Several Types of Ergodicity for M/G/1-Type Markov Chains and Markov Processes

2006 ◽  
Vol 43 (1) ◽  
pp. 141-158 ◽  
Author(s):  
Yuanyuan Liu ◽  
Zhenting Hou
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Generating Function ◽  
Final Section ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Radius Of Convergence ◽  
Exponential Ergodicity ◽  
Return Probability ◽  
Explicit Bounds

In this paper we study polynomial and geometric (exponential) ergodicity for M/G/1-type Markov chains and Markov processes. First, practical criteria for M/G/1-type Markov chains are obtained by analyzing the generating function of the first return probability to level 0. Then the corresponding criteria for M/G/1-type Markov processes are given, using their h-approximation chains. Our method yields the radius of convergence of the generating function of the first return probability, which is very important in obtaining explicit bounds on geometric (exponential) convergence rates. Our results are illustrated, in the final section, in some examples.

scholarly journals Exponential ergodicity for Markov processes with random switching

Bernoulli ◽  
2015 ◽  
Vol 21 (1) ◽  
pp. 505-536 ◽  
Author(s):  
Bertrand Cloez ◽  
Martin Hairer
Keyword(s):  
Markov Processes ◽  
Exponential Ergodicity ◽  
Random Switching

Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes

1981 ◽  
Vol 18 (1) ◽  
pp. 122-130 ◽  
Author(s):  
R. L. Tweedie
Keyword(s):  
Markov Processes ◽  
Existence Of Solutions ◽  
Strong Ergodicity ◽  
Exponential Ergodicity ◽  
Countable Space ◽  
Birth Death

For regular Markov processes on a countable space, we provide criteria for the forms of ergodicity in the title in terms of the existence of solutions to inequalities involving the Q-matrix of the process. An application to birth-death processes is given.

Exponential ergodicity of general Markov processes

1979 ◽  
Vol 11 (2) ◽  
pp. 279-280
Author(s):  
Pekka Tuominen ◽  
Richard L. Tweedie
Keyword(s):  
Markov Processes ◽  
Exponential Ergodicity

scholarly journals Several Types of Ergodicity for M/G/1-Type Markov Chains and Markov Processes

2006 ◽  
Vol 43 (01) ◽  
pp. 141-158 ◽  
Author(s):  
Yuanyuan Liu ◽  
Zhenting Hou
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Generating Function ◽  
Final Section ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Radius Of Convergence ◽  
Exponential Ergodicity ◽  
Return Probability ◽  
Explicit Bounds

In this paper we study polynomial and geometric (exponential) ergodicity for M/G/1-type Markov chains and Markov processes. First, practical criteria for M/G/1-type Markov chains are obtained by analyzing the generating function of the first return probability to level 0. Then the corresponding criteria for M/G/1-type Markov processes are given, using their h-approximation chains. Our method yields the radius of convergence of the generating function of the first return probability, which is very important in obtaining explicit bounds on geometric (exponential) convergence rates. Our results are illustrated, in the final section, in some examples.

Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes

1981 ◽  
Vol 18 (01) ◽  
pp. 122-130 ◽  
Author(s):  
R. L. Tweedie
Keyword(s):  
Markov Processes ◽  
Existence Of Solutions ◽  
Strong Ergodicity ◽  
Exponential Ergodicity ◽  
Countable Space ◽  
Birth Death

For regular Markov processes on a countable space, we provide criteria for the forms of ergodicity in the title in terms of the existence of solutions to inequalities involving the Q-matrix of the process. An application to birth-death processes is given.

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