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Random walk on a building of type Ãr and brownian motion of the Weyl chamber

Bruno Schapira (2009)

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

In this paper we study a random walk on an affine building of type Ãr, whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane (Probab. Theory Related Fields89 (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered by Bougerol...

Recollement de semi-groupes de Feller locaux

Jean-Pierre Roth (1980)

Annales de l'institut Fourier

Des semi-groupes de Feller locaux, deux à deux compatibles et définis sur des ouverts recouvrant un espace compact E , se recollent en un semi-groupe de Feller local unique défini sur E . Le principe du maximum joue un rôle essentiel dans la démonstration de ce résultat. Un théorème de recollement des générateurs infinitésimaux s’en déduit.

Recorridos aleatorios simples en tiempo continuo.

Ricardo Vélez Ibarrola (1983)

Trabajos de Estadística e Investigación Operativa

The properties of a certain generalization of simple random walk to continuous time are analyzed in this paper. After the definition, its transition probabilities, and the differential equations satisfied by those, are obtained. Under some conditions, the convergence of this random walk to a Wiener process is then established. Finally, absorption probabilities and mean times until absorption are calculated, giving some insight into the behaviour of the process.

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