Displaying similar documents to “Estimating powers with base close to unity and large exponents.”

Approximating real Pochhammer products: a comparison with powers

Vito Lampret (2009)

Open Mathematics

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Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.

Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley (2010)

ESAIM: Probability and Statistics

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We consider the approximation of a mean field stochastic process by a large interacting particle system. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around the law of the process. The method is based on a coupling argument, strong integrability estimates on the paths in Hölder norm, and a general concentration result for the empirical measure of identically distributed independent paths. ...

Potentials of a Markov process are expected suprema

Hans Föllmer, Thomas Knispel (2007)

ESAIM: Probability and Statistics

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Expected suprema of a function  observed along the paths of a nice Markov process define an excessive function, and in fact a potential if  vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus...

A Gronwall-like inequality and its applications

Adrian Constantin (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A generalized Gronwall-like inequality is established and applied in obtaining a right saturated solution for a class of differential equations and in estimating the solution of an evolution equation for the so called hidden variables.