scholarly journals A complete convergence theorem for stationary regularly varying multivariate time series

Extremes ◽  
2016 ◽  
Vol 19 (3) ◽  
pp. 549-560 ◽  
Author(s):  
Bojan Basrak ◽  
Azra Tafro
Keyword(s):  
Time Series ◽  
Convergence Theorem ◽  
Complete Convergence ◽  
Multivariate Time Series ◽  
Regularly Varying ◽  
Complete Convergence Theorem

scholarly journals On some threshold-one attractive interacting particle systems on homogeneous trees

2020 ◽  
Vol 57 (3) ◽  
pp. 866-898
Author(s):  
Y. X. Mu ◽  
Y. Zhang
Keyword(s):  
Convergence Theorem ◽  
Complete Convergence ◽  
Interacting Particle Systems ◽  
Initial Conditions ◽  
Contact Process ◽  
Particle Systems ◽  
Voter Model ◽  
Interacting Particle ◽  
Homogeneous Trees ◽  
Complete Convergence Theorem

AbstractWe consider the threshold-one contact process, the threshold-one voter model and the threshold-one voter model with positive spontaneous death on homogeneous trees $\mathbb{T}_d$ , $d\ge 2$ . Mainly inspired by the corresponding arguments for the contact process, we prove that the complete convergence theorem holds for these three systems under strong survival. When the system survives weakly, complete convergence may also hold under certain transition and/or initial conditions.

A Complete Convergence Theorem for Attractive Reversible Nearest Particle Systems

1997 ◽  
Vol 49 (2) ◽  
pp. 321-337 ◽  
Author(s):  
T. S. Mountford
Keyword(s):  
Convergence Theorem ◽  
Invariant Measures ◽  
Complete Convergence ◽  
Regularity Condition ◽  
Particle Systems ◽  
Complete Convergence Theorem

AbstractIn this paper we prove a complete convergence theorem for attractive, reversible, super-critical nearest particle systems satisfying a natural regularity condition. In particular this implies that under these conditions there exist precisely two extremal invariant measures. The result we prove is relevant to question seven of Liggett (1985), Chapter VII.

scholarly journals Regularly varying multivariate time series

2009 ◽  
Vol 119 (4) ◽  
pp. 1055-1080 ◽  
Author(s):  
Bojan Basrak ◽  
Johan Segers
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Regularly Varying

scholarly journals Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rong Hu ◽  
Qunying Wu
Keyword(s):  
Convergence Theorem ◽  
Probability Space ◽  
Complete Convergence ◽  
Choquet Integral ◽  
Random Variables ◽  
Weighted Sums ◽  
Sublinear Expectation ◽  
Acceptable Random Variables ◽  
Complete Convergence Theorem

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

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