Extreme Deviations and Applications

Extreme Deviations and Applications

Extreme deviations for sums of random variables

Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random multiplicative process. For this, a theory of extreme deviations is developed, devoted to the far tail of the pdf of the sum X of a finite number n of independen...

Large deviations of stochastic systems and applications

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Extreme Deviations from Expected Evolutionary Rates in Archaeal Protein Families

Origin of new biological functions is a complex phenomenon ranging from single-nucleotide substitutions to the gain of new genes via horizontal gene transfer or duplication. Neofunctionalization and subfunctionalization of proteins is often attributed to the emergence of paralogs that are subject to relaxed purifying selection or positive selection and thus evolve at accelerated rates. Such phe...

2 Extreme deviations for sums of random variables

Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random multiplicative process. For this, a theory of extreme deviations is developed, devoted to the far tail of the pdf of the sum X of a finite number n of independen...