Large Deviation Principle for Exchangeable Sequences: Necessary and Sufficient Condition

2004 ◽  
Vol 17 (4) ◽  
pp. 967-978 ◽  
Author(s):  
L. Wu
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Deviation Principle ◽  
Necessary And Sufficient

scholarly journals On asymptotically efficient simulation of large deviation probabilities

2005 ◽  
Vol 37 (2) ◽  
pp. 539-552 ◽  
Author(s):  
A. B. Dieker ◽  
M. Mandjes
Keyword(s):  
Importance Sampling ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Sampling Distribution ◽  
Efficient Simulation ◽  
Deviation Principle ◽  
Asymptotically Efficient Estimator ◽  
Asymptotically Efficient ◽  
Necessary And Sufficient

Let {νε, ε>0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable set A and some ε0>0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

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 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 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.

scholarly journals On asymptotically efficient simulation of large deviation probabilities

2005 ◽  
Vol 37 (02) ◽  
pp. 539-552 ◽  
Author(s):  
A. B. Dieker ◽  
M. Mandjes
Keyword(s):  
Importance Sampling ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Sampling Distribution ◽  
Efficient Simulation ◽  
Deviation Principle ◽  
Asymptotically Efficient Estimator ◽  
Asymptotically Efficient ◽  
Necessary And Sufficient

Let {νε, ε&gt;0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable setAand some ε0&gt;0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

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