scholarly journals Exponential ergodicity and strong ergodicity for SDEs driven by symmetricα-stable processes

2013 ◽  
Vol 26 (6) ◽  
pp. 654-658 ◽  
Author(s):  
Jian Wang
Keyword(s):  
Stable Processes ◽  
Strong Ergodicity ◽  
Exponential Ergodicity

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 for population dynamics driven byα-stable processes

2017 ◽  
Vol 125 ◽  
pp. 149-159 ◽  
Author(s):  
Zhenzhong Zhang ◽  
Xuekang Zhang ◽  
Jinying Tong
Keyword(s):  
Population Dynamics ◽  
Stable Processes ◽  
Exponential Ergodicity

scholarly journals Lyapunov-type conditions for non-strong ergodicity of Markov processes

2021 ◽  
Vol 58 (1) ◽  
pp. 238-253
Author(s):  
Yong-Hua Mao ◽  
Tao Wang
Keyword(s):  
Markov Processes ◽  
Riemannian Manifolds ◽  
Diffusion Processes ◽  
Stable Processes ◽  
Strong Ergodicity ◽  
Stable Noise

AbstractWe present Lyapunov-type conditions for non-strong ergodicity of Markov processes. Some concrete models are discussed, including diffusion processes on Riemannian manifolds and Ornstein–Uhlenbeck processes driven by symmetric $\alpha$-stable processes. In particular, we show that any process of d-dimensional Ornstein–Uhlenbeck type driven by $\alpha$-stable noise is not strongly ergodic for every $\alpha\in (0,2]$.

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.

Population dynamics driven by truncated stable processes with Markovian switching

2021 ◽  
Vol 58 (2) ◽  
pp. 505-522
Author(s):  
Zhenzhong Zhang ◽  
Jinying Tong ◽  
Qingting Meng ◽  
You Liang
Keyword(s):  
Population Dynamics ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Markovian Switching ◽  
Stable Processes ◽  
Necessary And Sufficient ◽  
The Impact

AbstractWe focus on the population dynamics driven by two classes of truncated $\alpha$-stable processes with Markovian switching. Almost necessary and sufficient conditions for the ergodicity of the proposed models are provided. Also, these results illustrate the impact on ergodicity and extinct conditions as the parameter $\alpha$ tends to 2.

scholarly journals A generalization of Matérn hard-core processes with applications to max-stable processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1298-1312
Author(s):  
Martin Dirrler ◽  
Christopher Dörr ◽  
Martin Schlather
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Hard Core ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Poisson Point Processes ◽  
Original Process ◽  
Mixed Moving Maxima

AbstractMatérn hard-core processes are classical examples for point processes obtained by dependent thinning of (marked) Poisson point processes. We present a generalization of the Matérn models which encompasses recent extensions of the original Matérn hard-core processes. It generalizes the underlying point process, the thinning rule, and the marks attached to the original process. Based on our model, we introduce processes with a clear interpretation in the context of max-stable processes. In particular, we prove that one of these processes lies in the max-domain of attraction of a mixed moving maxima process.

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