scholarly journals Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes

2013 ◽  
Vol 154 (4) ◽  
pp. 929-949 ◽  
Author(s):  
Zhao Dong ◽  
Lihu Xu ◽  
Xicheng Zhang
Keyword(s):  
Stable Processes ◽  
Burgers Equations ◽  
Exponential Ergodicity

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

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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