scholarly journals Moderate deviations of density-dependent Markov chains

2021 ◽  
Author(s):  
Xiaofeng Xue
Keyword(s):  
Markov Chains ◽  
Moderate Deviations ◽  
Density Dependent

scholarly journals Large and moderate deviations for bounded functions of slowly mixing Markov chains

2017 ◽  
Vol 18 (02) ◽  
pp. 1850017
Author(s):  
Jérôme Dedecker ◽  
Sébastien Gouëzel ◽  
Florence Merlevède
Keyword(s):  
Probability Theory ◽  
Dynamical Systems ◽  
Markov Chains ◽  
Weak Sense ◽  
Moderate Deviations ◽  
Mixing Speed ◽  
Bounded Functions

We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities. These inequalities can be applied in various natural situations coming from probability theory or dynamical systems. Finally, we discuss examples from these various settings showing that our inequalities are sharp.

scholarly journals Moderate Deviations for Word Counts in Biological Sequences

2009 ◽  
Vol 46 (04) ◽  
pp. 1020-1037
Author(s):  
Sarah Behrens ◽  
Matthias Löwe
Keyword(s):  
Markov Chains ◽  
Dna Sequences ◽  
Protein Sequences ◽  
Moderate Deviation ◽  
Moderate Deviations ◽  
Biological Sequences ◽  
Transition Matrices ◽  
P Values ◽  
Moderate Deviation Principle ◽  
Deviation Principle

We derive a moderate deviation principle for word counts (which is extended to counts of multiple patterns) in biological sequences under different models: independent and identically distributed letters, homogeneous Markov chains of order 1 and m, and, in view of the codon structure of DNA sequences, Markov chains with three different transition matrices. This enables us to approximate P-values for the number of word occurrences in DNA and protein sequences in a new manner.

scholarly journals Moderate Deviations for Word Counts in Biological Sequences

2009 ◽  
Vol 46 (4) ◽  
pp. 1020-1037 ◽  
Author(s):  
Sarah Behrens ◽  
Matthias Löwe
Keyword(s):  
Markov Chains ◽  
Dna Sequences ◽  
Protein Sequences ◽  
Moderate Deviation ◽  
Moderate Deviations ◽  
Biological Sequences ◽  
Transition Matrices ◽  
P Values ◽  
Moderate Deviation Principle ◽  
Deviation Principle

We derive a moderate deviation principle for word counts (which is extended to counts of multiple patterns) in biological sequences under different models: independent and identically distributed letters, homogeneous Markov chains of order 1 and m, and, in view of the codon structure of DNA sequences, Markov chains with three different transition matrices. This enables us to approximate P-values for the number of word occurrences in DNA and protein sequences in a new manner.

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