CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: LP -APPROXIMABILITY VERSUS BROWNIAN MOTION

2009 ◽  
Vol 25 (3) ◽  
pp. 748-763 ◽  
Author(s):  
Kairat T. Mynbaev
Keyword(s):  
Brownian Motion ◽  
Central Limit ◽  
Asymptotic Expansions ◽  
Limit Theorems ◽  
Stochastic Calculus ◽  
Central Limit Theorems ◽  
Weighted Sums ◽  
Linear Processes

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

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.

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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