A functional ergodic theorem for the occupation time process of a branching system

2008 ◽  
Vol 78 (7) ◽  
pp. 847-853 ◽  
Author(s):  
Anna Talarczyk
Keyword(s):  
Ergodic Theorem ◽  
Occupation Time ◽  
Time Process ◽  
Branching System ◽  
Occupation Time Process

Limit theorems for alternating renewal processes in the infinite mean case

2001 ◽  
Vol 33 (4) ◽  
pp. 896-911 ◽  
Author(s):  
K. V. Mitov ◽  
N. M. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Limit Theorems ◽  
Occupation Time ◽  
Renewal Processes ◽  
Time Process ◽  
Asymptotic Results ◽  
Mean Cycle ◽  
New Phenomena ◽  
Occupation Time Process

The asymptotic behaviour of an occupation-time process associated with alternating renewal processes is investigated in the infinite mean cycle case. The limit theorems obtained extend some asymptotic results proved by Dynkin (1955), Lamperti (1958) and Erickson (1970) for the classical spent lifetime process. Some new phenomena are also presented.

LARGE AND MODERATE DEVIATIONS FOR OCCUPATION TIMES OF IMMIGRATION SUPERPROCESSES

2005 ◽  
Vol 08 (04) ◽  
pp. 593-603 ◽  
Author(s):  
WENMING HONG ◽  
ZENGHU LI
Keyword(s):  
Moderate Deviation ◽  
Moderate Deviations ◽  
Occupation Time ◽  
Time Process ◽  
Occupation Times ◽  
Occupation Time Process

Large and moderate deviation principles are proved for the occupation time process of a subcritical branching superprocess with immigration.

Limit theorems for alternating renewal processes in the infinite mean case

2001 ◽  
Vol 33 (04) ◽  
pp. 896-911 ◽  
Author(s):  
K. V. Mitov ◽  
N. M. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Limit Theorems ◽  
Occupation Time ◽  
Renewal Processes ◽  
Time Process ◽  
Asymptotic Results ◽  
Mean Cycle ◽  
New Phenomena ◽  
Occupation Time Process

The asymptotic behaviour of an occupation-time process associated with alternating renewal processes is investigated in the infinite mean cycle case. The limit theorems obtained extend some asymptotic results proved by Dynkin (1955), Lamperti (1958) and Erickson (1970) for the classical spent lifetime process. Some new phenomena are also presented.

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.

scholarly journals A generalized occupation time formula for continuous semimartingales

2010 ◽  
Vol 47 (1) ◽  
pp. 54-58
Author(s):  
Raouf Ghomrasni
Keyword(s):  
Local Time ◽  
Wide Class ◽  
Quadratic Variation ◽  
Occupation Time ◽  
Time Process ◽  
Continuous Semimartingale ◽  
Class Of Functions ◽  
Variation Process

We show that for a wide class of functions F we have lim \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\lim }\limits_{\varepsilon \downarrow 0} \frac{1}{\varepsilon }\int\limits_0^t {\{ F(s,X_s ) - F(s,X_s - \varepsilon )\} d\left\langle {X,X} \right\rangle _s = - } \int\limits_0^t {\int\limits_\mathbb{R} {F(s,x)dL_s^x } }$$ \end{document} where Xt is a continuous semimartingale, ( Ltx , x ∈ ℝ, t ≧ 0) its local time process and (〈 X, X 〉 t , t ≧ 0) its quadratic variation process.

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.

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