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Regularity of irregularities on a brownian path

Samuel James Taylor (1974)

Annales de l'institut Fourier

On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed t 0 with probability 1. This paper is a survey of recent results which quantity the extent of the irregularities and show that the exceptional points themselves occur in an extremely regular manner.

Reinforced walk on graphs and neural networks

Józef Myjak, Ryszard Rudnicki (2008)

Studia Mathematica

A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.

Remarks on the boolean convolution and Kerov's α-transformation

Anna Dorota Krystek (2006)

Banach Center Publications

This paper consists of two parts. The first part is devoted to the study of continuous diagrams and their connections with the boolean convolution. In the second part we investigate the rectangular Young diagrams and respective discrete measures. We recall the definition of Kerov's α-transformation of diagrams, define the α-transformation of finitely supported discrete measures and generalize the notion of the α-transformation.

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