The oscillation of the occupation time process of super- Brownian motion on Sierpinski gasket

2000 ◽  
Vol 43 (12) ◽  
pp. 1250-1257
Author(s):  
Junyi Guo
Keyword(s):  
Brownian Motion ◽  
Sierpinski Gasket ◽  
Occupation Time ◽  
Time Process ◽  
Sierpiński Gasket ◽  
Super Brownian Motion ◽  
Occupation Time Process

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.

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 (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 Brownian motion on a random recursive Sierpinski gasket

1997 ◽  
Vol 25 (3) ◽  
pp. 1059-1102 ◽  
Author(s):  
B. M. Hambly
Keyword(s):  
Brownian Motion ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket
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