scholarly journals Longtime behavior for the occupation time process of a super-Brownian motion with random immigration

2002 ◽  
Vol 102 (1) ◽  
pp. 43-62 ◽  
Author(s):  
Wenming Hong
Keyword(s):  
Brownian Motion ◽  
Occupation Time ◽  
Time Process ◽  
Super Brownian Motion ◽  
Longtime Behavior ◽  
Occupation Time Process ◽  
Random Immigration

Large deviations for super-Brownian motion with immigration

2004 ◽  
Vol 41 (01) ◽  
pp. 187-201 ◽  
Author(s):  
Mei Zhang
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Lebesgue Measure ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Time Process ◽  
Super Brownian Motion ◽  
Speed Function ◽  
Occupation Time Process ◽  
Random Immigration

We derive a large-deviation principle for super-Brownian motion with immigration, where the immigration is governed by the Lebesgue measure. We show that the speed function ist1/2ford= 1,t/logtford= 2 andtford≥ 3, which is different from that of the occupation-time process counterpart (without immigration) and the model of random immigration.

Large deviations for super-Brownian motion with immigration

2004 ◽  
Vol 41 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Mei Zhang
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Lebesgue Measure ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Time Process ◽  
Super Brownian Motion ◽  
Speed Function ◽  
Occupation Time Process ◽  
Random Immigration

We derive a large-deviation principle for super-Brownian motion with immigration, where the immigration is governed by the Lebesgue measure. We show that the speed function is t1/2 for d = 1, t/logt for d = 2 and t for d ≥ 3, which is different from that of the occupation-time process counterpart (without immigration) and the model of random immigration.

Occupation time processes of super-Brownian motion with cut-off branching

2004 ◽  
Vol 41 (4) ◽  
pp. 984-997 ◽  
Author(s):  
Zhao Dong ◽  
Shui Feng
Keyword(s):  
Brownian Motion ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Rate Function ◽  
Occupation Time ◽  
Time Behavior ◽  
Long Time ◽  
Super Brownian Motion ◽  
Dimension One ◽  
Occupation Time Process

In this article we investigate a class of superprocess with cut-off branching, studying the long-time behavior of the occupation time process. Persistence of the process holds in all dimensions. Central-limit-type theorems are obtained, and the scales are dimension dependent. The Gaussian limit holds only when d ≤ 4. In dimension one, a full large deviation principle is established and the rate function is identified explicitly. Our result shows that the super-Brownian motion with cut-off branching in dimension one has many features that are similar to super-Brownian motion in dimension three.

Occupation time processes of super-Brownian motion with cut-off branching

2004 ◽  
Vol 41 (04) ◽  
pp. 984-997
Author(s):  
Zhao Dong ◽  
Shui Feng
Keyword(s):  
Brownian Motion ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Rate Function ◽  
Occupation Time ◽  
Time Behavior ◽  
Long Time ◽  
Super Brownian Motion ◽  
Dimension One ◽  
Occupation Time Process

In this article we investigate a class of superprocess with cut-off branching, studying the long-time behavior of the occupation time process. Persistence of the process holds in all dimensions. Central-limit-type theorems are obtained, and the scales are dimension dependent. The Gaussian limit holds only when d ≤ 4. In dimension one, a full large deviation principle is established and the rate function is identified explicitly. Our result shows that the super-Brownian motion with cut-off branching in dimension one has many features that are similar to super-Brownian motion in dimension three.

A LARGE DEVIATION FOR OCCUPATION TIME OF SUPER α-STABLE PROCESS

2008 ◽  
Vol 11 (01) ◽  
pp. 53-71 ◽  
Author(s):  
QIU-YUE LI ◽  
YAN-XIA REN
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stable Process ◽  
Rate Function ◽  
Occupation Time ◽  
Occupation Times ◽  
Tail Probabilities ◽  
Super Brownian Motion

We derive a large deviation principle for occupation time of super α-stable process in ℝd with d > 2α. The decay of tail probabilities is shown to be exponential and the rate function is characterized. Our result can be considered as a counterpart of Lee's work on large deviations for occupation times of super-Brownian motion in ℝd for dimension d > 4 (see Ref. 10).

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.

QUENCHED LARGE DEVIATION FOR SUPER-BROWNIAN MOTION WITH RANDOM IMMIGRATION

2008 ◽  
Vol 11 (04) ◽  
pp. 627-637
Author(s):  
WENMING HONG
Keyword(s):  
Brownian Motion ◽  
Large Deviation ◽  
Critical Dimension ◽  
Super Brownian Motion ◽  
Random Immigration

Quenched local large deviation is derived for the super-Brownian motion with super-Brownian immigration, in dimension d ≥ 4. At the critical dimension d = 4, the quenched and annealed LDP are of the same speed but are different rate.

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