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

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.

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 CIR interest rate model with random switching

2016 ◽  
Vol 17 (05) ◽  
pp. 1750037 ◽  
Author(s):  
Jinying Tong ◽  
Zhenzhong Zhang
Keyword(s):  
Interest Rate ◽  
Stationary Distribution ◽  
Wasserstein Distance ◽  
Transition Semigroup ◽  
Rate Model ◽  
Cir Model ◽  
Exponential Ergodicity ◽  
The Central Limit Theorem ◽  
Random Switching ◽  
Interest Rate Model

In this paper, we consider ergodicity of Cox–Ingersoll–Ross (CIR) interest rate model with random switching. First, we show that the CIR model with switching has a unique stationary distribution. Next, we prove that the transition semigroup for the CIR model with switching converges to the stationary distribution at an exponential rate in the Wasserstein distance. Moreover, under two particular cases, the explicit expressions for stationary distributions are presented. Finally, the central limit theorem for the CIR model with random switching is established.

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 Random switching near bifurcations

2019 ◽  
Vol 20 (02) ◽  
pp. 2050008 ◽  
Author(s):  
Tobias Hurth ◽  
Christian Kuehn
Keyword(s):  
Markov Processes ◽  
Vector Fields ◽  
Invariant Measures ◽  
Blow Up ◽  
Nonlinear Models ◽  
Switching Dynamics ◽  
Piecewise Deterministic Markov Processes ◽  
Random Switching ◽  
Pitchfork Bifurcations

The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise-deterministic Markov processes arising from stochastic switching dynamics near fold, Hopf, transcritical and pitchfork bifurcations. We prove the existence of invariant measures for different switching rates. We also study when the invariant measures are unique, when multiple measures occur, when measures have smooth densities, and under which conditions finite-time blow-up occurs. We demonstrate the applicability of our results for three nonlinear models arising in applications.

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.

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

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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