scholarly journals A large deviation principle for a Brownian immigration particle system

2005 ◽  
Vol 42 (04) ◽  
pp. 1120-1133
Author(s):  
Mei Zhang
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Particle System ◽  
Random Measure ◽  
Poisson Random Measure ◽  
Intensity Measure ◽  
Branching Particle System ◽  
Deviation Principle

We derive a large deviation principle for a Brownian immigration branching particle system, where the immigration is governed by a Poisson random measure with a Lebesgue intensity measure.

scholarly journals A large deviation principle for a Brownian immigration particle system

2005 ◽  
Vol 42 (4) ◽  
pp. 1120-1133
Author(s):  
Mei Zhang
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Particle System ◽  
Random Measure ◽  
Poisson Random Measure ◽  
Intensity Measure ◽  
Branching Particle System ◽  
Deviation Principle

We derive a large deviation principle for a Brownian immigration branching particle system, where the immigration is governed by a Poisson random measure with a Lebesgue intensity measure.

Immigration processes associated with branching particle systems

1998 ◽  
Vol 30 (03) ◽  
pp. 657-675 ◽  
Author(s):  
Zeng-Hu Li
Keyword(s):  
Particle System ◽  
Random Measure ◽  
Particle Systems ◽  
Poisson Random Measure ◽  
General Representation ◽  
Branching Particle System ◽  
Convolution Semigroups ◽  
Entrance Law ◽  
Skew Convolution Semigroup ◽  
Special Case

The immigration processes associated with a given branching particle system are formulated by skew convolution semigroups. It is shown that every skew convolution semigroup corresponds uniquely to a locally integrable entrance law for the branching particle system. The immigration particle system may be constructed using a Poisson random measure based on a Markovian measure determined by the entrance law. In the special case where the underlying process is a minimal Brownian motion in a bounded domain, a general representation is given for locally integrable entrance laws for the branching particle system. The convergence of immigration particle systems to measure-valued immigration processes is also studied.

Large deviation principle for semilinear stochastic evolution equations with Poisson noise

2017 ◽  
Vol 20 (02) ◽  
pp. 1750009
Author(s):  
Hassan Dadashi
Keyword(s):  
Evolution Equations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Functional Differential Equations ◽  
Random Measure ◽  
Poisson Noise ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Deviation Principle ◽  
Wide Range

We demonstrate the large deviation principle in the small noise limit for the mild solution of semilinear stochastic evolution equations with monotone nonlinearity and multiplicative Poisson noise. A recently developed method in studying the large deviation principle, weak convergent method, is employed. We apply the result obtained by Budhiraja et al.,7 that reveals the variational representation of exponential integrals w.r.t. the Poisson random measure. Our framework covers a wide range of parabolic, hyperbolic and functional differential equations. We give some examples to illustrate the applications of our results.

Immigration processes associated with branching particle systems

1998 ◽  
Vol 30 (3) ◽  
pp. 657-675 ◽  
Author(s):  
Zeng-Hu Li
Keyword(s):  
Particle System ◽  
Random Measure ◽  
Particle Systems ◽  
Poisson Random Measure ◽  
General Representation ◽  
Branching Particle System ◽  
Convolution Semigroups ◽  
Entrance Law ◽  
Skew Convolution Semigroup ◽  
Special Case

The immigration processes associated with a given branching particle system are formulated by skew convolution semigroups. It is shown that every skew convolution semigroup corresponds uniquely to a locally integrable entrance law for the branching particle system. The immigration particle system may be constructed using a Poisson random measure based on a Markovian measure determined by the entrance law. In the special case where the underlying process is a minimal Brownian motion in a bounded domain, a general representation is given for locally integrable entrance laws for the branching particle system. The convergence of immigration particle systems to measure-valued immigration processes is also studied.

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

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.

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