scholarly journals A CLT for dependent random variables with an application to an infinite system of interacting diffusion processes

2021 ◽  
Vol 149 (12) ◽  
pp. 5367-5384
Author(s):  
Le Chen ◽  
Davar Khoshnevisan ◽  
David Nualart ◽  
Fei Pu
Keyword(s):  
Infinite System ◽  
Diffusion Processes ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Interacting Diffusion

An L2-approximation method for construction and smoothing estimates of Markov semigroups for interacting diffusion processes on a lattice

2021 ◽  
Vol 24 (01) ◽  
pp. 2150004
Author(s):  
Yong Sul Won
Keyword(s):  
Infinite System ◽  
Nearest Neighbor ◽  
Diffusion Processes ◽  
Mathematical Problem ◽  
Markov Semigroups ◽  
Propagation Property ◽  
Finite Speed Of Propagation ◽  
Pointwise Estimation ◽  
Interacting Diffusion ◽  
Speed Of Propagation

We develop an [Formula: see text]-approximation strategy to study Markov semigroups generated by an infinite system of elliptic diffusion processes on a lattice. The proposed dynamics incorporate nearest neighbor interactions influencing diffusivity, which has received little attention so far as a mathematical problem. We prove the existence and the smoothness of Markov semigroups by extending the well-known pointwise estimation techniques such as the finite speed of propagation property and the Lyapunov function methods.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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