Central Limit Theorem and Moderate Deviations for a Class of Semilinear Stochastic Partial Differential Equations

2020 ◽  
Vol 40 (5) ◽  
pp. 1477-1494
Author(s):  
Shulan Hu ◽  
Ruinan Li ◽  
Xinyu Wang
Keyword(s):  
Central Limit Theorem ◽  
Partial Differential Equations ◽  
Limit Theorem ◽  
Differential Equations ◽  
Central Limit ◽  
Stochastic Partial Differential Equations ◽  
Moderate Deviations ◽  
Partial Differential

An elementary proof of Peng’s central limit theorem under sub-linear expectations

2020 ◽  
Vol 07 (02) ◽  
pp. 2050020
Author(s):  
Zengjing Chen ◽  
Ziwu Zhang
Keyword(s):  
Central Limit Theorem ◽  
Partial Differential Equations ◽  
Limit Theorem ◽  
Differential Equations ◽  
Central Limit ◽  
Elementary Proof ◽  
Random Variables ◽  
Mathematical Finance ◽  
Partial Differential ◽  
Reasonable Condition

Motivated by studies in mathematical finance, S. Peng established a central limit theorem (CLT) under sub-linear expectations by using partial differential equations (PDEs). In this paper, we provide a novel proof of Peng’s CLT in the frame of sub-linear expectation. Our method is not only elementary in the sense that it does not use PDEs, but also more applicable because we only require the random variables to satisfy a reasonable condition which coincides with the classical Lindeberg’s condition when the sub-linear expectation reduces to a linear expectation.

scholarly journals Central limit theorem for a class of SPDEs

2015 ◽  
Vol 52 (3) ◽  
pp. 786-796 ◽  
Author(s):  
Parisa Fatheddin
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Partial Differential Equations ◽  
Limit Theorem ◽  
Differential Equations ◽  
Central Limit ◽  
Stochastic Partial Differential Equations ◽  
Population Models ◽  
The Central Limit Theorem ◽  
Super Brownian Motion

In this paper we establish the central limit theorem for a class of stochastic partial differential equations and as an application derive this theorem for two widely studied population models: super-Brownian motion and the Fleming-Viot process.

scholarly journals Central limit theorem for a class of SPDEs

2015 ◽  
Vol 52 (03) ◽  
pp. 786-796 ◽  
Author(s):  
Parisa Fatheddin
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Partial Differential Equations ◽  
Limit Theorem ◽  
Differential Equations ◽  
Central Limit ◽  
Stochastic Partial Differential Equations ◽  
Population Models ◽  
The Central Limit Theorem ◽  
Super Brownian Motion

In this paper we establish the central limit theorem for a class of stochastic partial differential equations and as an application derive this theorem for two widely studied population models: super-Brownian motion and the Fleming-Viot process.

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