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.

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.

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).

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.

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
Author(s):  
A. A. DOROGOVTSEV ◽  
O. V. OSTAPENKO
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Flows ◽  
Brownian Motions ◽  
Deviation Principle ◽  
And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

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.

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).

ON A SUFFICIENT CONDITION FOR LARGE DEVIATIONS OF ADDITIVE FUNCTIONALS

2011 ◽  
Vol 11 (01) ◽  
pp. 157-181 ◽  
Author(s):  
KANEHARU TSUCHIDA
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Markov Processes ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stable Processes ◽  
Sufficient Condition ◽  
Additive Functionals ◽  
Deviation Principle ◽  
Symmetric Markov Processes

We prove the large deviation principle for continuous additive functionals under certain assumptions. The underlying symmetric Markov processes include Brownian motion and symmetric and relativistic α-stable processes.

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