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Transient random walk in 2 with stationary orientations

Françoise Pène (2009)

ESAIM: Probability and Statistics

In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412]. We study a random walk in 2 with random orientations. We suppose that the orientation of the kth floor is given by ξ k , where ( ξ k ) k is a stationary sequence of random variables. Once the environment fixed, the random walk can go either up or down or can stay in the present floor (but moving with respect to its orientation). This model was introduced by Campanino and Pétritis in [Markov Process....

Transitions on a noncompact Cantor set and random walks on its defining tree

Jun Kigami (2013)

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

First, noncompact Cantor sets along with their defining trees are introduced as a natural generalization of p -adic numbers. Secondly we construct a class of jump processes on a noncompact Cantor set from given pairs of eigenvalues and measures. At the same time, we have concrete expressions of the associated jump kernels and transition densities. Then we construct intrinsic metrics on noncompact Cantor set to obtain estimates of transition densities and jump kernels under some regularity conditions...

Transportation inequalities for stochastic differential equations of pure jumps

Liming Wu (2010)

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

For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that W1H transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the L1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.

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