A central limit theorem for super-Brownian motion with super-Brownian immigration

1999 ◽  
Vol 36 (4) ◽  
pp. 1218-1224 ◽  
Author(s):  
Wen-Ming Hong ◽  
Zeng-Hu Li
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Potential Operator ◽  
Super Brownian Motion

We prove a central limit theorem for the super-Brownian motion with immigration governed by another super-Brownian. The limit theorem leads to Gaussian random fields in dimensions d ≥ 3. For d = 3 the field is spatially uniform; for d ≥ 5 its covariance is given by the potential operator of the underlying Brownian motion; and for d = 4 it involves a mixture of the two kinds of fluctuations.

A central limit theorem for super-Brownian motion with super-Brownian immigration

1999 ◽  
Vol 36 (04) ◽  
pp. 1218-1224 ◽  
Author(s):  
Wen-Ming Hong ◽  
Zeng-Hu Li
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Potential Operator ◽  
Super Brownian Motion

We prove a central limit theorem for the super-Brownian motion with immigration governed by another super-Brownian. The limit theorem leads to Gaussian random fields in dimensions d ≥ 3. For d = 3 the field is spatially uniform; for d ≥ 5 its covariance is given by the potential operator of the underlying Brownian motion; and for d = 4 it involves a mixture of the two kinds of fluctuations.

A note on two-level superprocesses

2004 ◽  
Vol 41 (1) ◽  
pp. 202-210
Author(s):  
Wen-Ming Hong
Keyword(s):  
Brownian Motion ◽  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Gaussian Random Fields ◽  
Central Limit Theorems ◽  
Gaussian Fields ◽  
Super Brownian Motion ◽  
Random Immigration

We prove some central limit theorems for a two-level super-Brownian motion with random immigration, which lead to limiting Gaussian random fields. The covariances of those Gaussian fields are explicitly characterized.

Moderate deviation for super-Brownian Motion with super-Brownian immigration

2002 ◽  
Vol 39 (04) ◽  
pp. 829-838 ◽  
Author(s):  
Wen-Ming Hong
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Large Deviation ◽  
Moderate Deviation ◽  
The Central Limit Theorem ◽  
Large Deviation Principles ◽  
Super Brownian Motion ◽  
Random Immigration

Moderate deviation principles are established in dimensionsd≥ 3 for super-Brownian motion with random immigration, where the immigration rate is governed by the trajectory of another super-Brownian motion. It fills in the gap between the central limit theorem and large deviation principles for this model which were obtained by Hong and Li (1999) and Hong (2001).

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.

A note on two-level superprocesses

2004 ◽  
Vol 41 (01) ◽  
pp. 202-210
Author(s):  
Wen-Ming Hong
Keyword(s):  
Brownian Motion ◽  
Central Limit ◽  
Random Fields ◽  
Limit Theorems ◽  
Gaussian Random Fields ◽  
Central Limit Theorems ◽  
Gaussian Fields ◽  
Super Brownian Motion ◽  
Random Immigration

We prove some central limit theorems for a two-level super-Brownian motion with random immigration, which lead to limiting Gaussian random fields. The covariances of those Gaussian fields are explicitly characterized.

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