scholarly journals Large deviation principle for stochastic Burgers type equation with reflection

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ran Wang ◽  
Jianliang Zhai ◽  
Shiling Zhang
Keyword(s):  
Weak Convergence ◽  
Multiplicative Noise ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Type Equation ◽  
Sufficient Condition ◽  
Convergence Criteria ◽  
Linear Coefficient ◽  
Deviation Principle ◽  
Non Linear

<p style='text-indent:20px;'>In this paper, we establish a large deviation principle for stochastic Burgers type equation with reflection perturbed by the small multiplicative noise. The main difficulties come from the highly non-linear coefficient and the singularity caused by the reflection. Here, we adopt a new sufficient condition for the weak convergence criteria, which is proposed by Matoussi, Sabbagh and Zhang [<xref ref-type="bibr" rid="b14">14</xref>].</p>

scholarly journals Large deviations for stochastic integrodifferential equations of the Itô type with multiple randomness

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 473-487 ◽  
Author(s):  
A. Haseena ◽  
M. Suvinthra ◽  
N. Annapoorani
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Finite Number ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Integrodifferential Equations ◽  
Multiplicative Noises ◽  
Deviation Principle ◽  
Laplace Principle ◽  
Weak Convergence Approach

A Freidlin-Wentzell type large deviation principle is derived for a class of It? type stochastic integrodifferential equations driven by a finite number of multiplicative noises of the Gaussian type. The weak convergence approach is used here to prove the Laplace principle, equivalently large deviation principle.

scholarly journals A Markov Chain Analysis of Genetic Algorithms: Large Deviation Principle Approach

2010 ◽  
Vol 47 (04) ◽  
pp. 967-975
Author(s):  
Joe Suzuki
Keyword(s):  
Genetic Algorithms ◽  
Markov Chain ◽  
Large Deviation Principle ◽  
Selective Pressure ◽  
Large Deviation ◽  
Sufficient Condition ◽  
Deviation Principle ◽  
Chain Analysis ◽  
Fitness Value ◽  
Uniform Population

In this paper we prove that the stationary distribution of populations in genetic algorithms focuses on the uniform population with the highest fitness value as the selective pressure goes to ∞ and the mutation probability goes to 0. The obtained sufficient condition is based on the work of Albuquerque and Mazza (2000), who, following Cerf (1998), applied the large deviation principle approach (Freidlin-Wentzell theory) to the Markov chain of genetic algorithms. The sufficient condition is more general than that of Albuquerque and Mazza, and covers a set of parameters which were not found by Cerf.

scholarly journals A Markov Chain Analysis of Genetic Algorithms: Large Deviation Principle Approach

2010 ◽  
Vol 47 (4) ◽  
pp. 967-975 ◽  
Author(s):  
Joe Suzuki
Keyword(s):  
Genetic Algorithms ◽  
Markov Chain ◽  
Large Deviation Principle ◽  
Selective Pressure ◽  
Large Deviation ◽  
Sufficient Condition ◽  
Deviation Principle ◽  
Chain Analysis ◽  
Fitness Value ◽  
Uniform Population

In this paper we prove that the stationary distribution of populations in genetic algorithms focuses on the uniform population with the highest fitness value as the selective pressure goes to ∞ and the mutation probability goes to 0. The obtained sufficient condition is based on the work of Albuquerque and Mazza (2000), who, following Cerf (1998), applied the large deviation principle approach (Freidlin-Wentzell theory) to the Markov chain of genetic algorithms. The sufficient condition is more general than that of Albuquerque and Mazza, and covers a set of parameters which were not found by Cerf.

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.

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.

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