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A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, , ( t )t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (theσ-algebra generated by ( t )t≥0) a coherent family of probability measures ( t ) indexed byt≥0, each of them being defined on t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual augmentation....

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Let (Ω, , ( t )t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (the σ-algebra generated by ( t )t≥0) a coherent family of probability measures ( t ) indexed by t≥0, each of them being defined on t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual...

A Riemann approach to random variation

Patrick Muldowney (2006)

Mathematica Bohemica

This essay outlines a generalized Riemann approach to the analysis of random variation and illustrates it by a construction of Brownian motion in a new and simple manner.

An algebraic approach to Pólya processes

Nicolas Pouyanne (2008)

Annales de l'I.H.P. Probabilités et statistiques

Pólya processes are natural generalizations of Pólya–Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference transition operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small when 1 is a simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part ≤1/2; otherwise, it is called large).

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