Central limit theorem for weighted local time of modulus of fractional Brownian motion

2012 ◽  
Vol 41 (4) ◽  
pp. 451-458 ◽  
Author(s):  
Chao Chen ◽  
Litan Yan ◽  
Cheng Ju
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Central Limit

scholarly journals Limit theorems for a quadratic variation of Gaussian processes

2011 ◽  
Vol 16 (4) ◽  
pp. 435-452 ◽  
Author(s):  
Raimondas Malukas
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Fractional Brownian Motion ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Quadratic Variation

In the paper a weighted quadratic variation based on a sequence of partitions for a class of Gaussian processes is considered. Conditions on the sequence of partitions and the process are established for the quadratic variation to converge almost surely and for a central limit theorem to be true. Also applications to bifractional and sub-fractional Brownian motion and the estimation of their parameters are provided.

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.

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).

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