Cénac, Peggy Le Ny, Arnaud de Loynes, Basile Offret, Yoann
Published in
Journal of Theoretical Probability

We consider a walker on the line that at each step keeps the same direction with a probability which depends on the time already spent in the direction the walker is currently moving. These walks with memories of variable length can be seen as generalizations of directionally reinforced random walks introduced in Mauldin et al. (Adv Math 117(2):239...

Mountford, Thomas S.
Published in
Journal of Theoretical Probability

We establish the correct Hausdorff measure function for the level sets of additive strictly stable processes derived from strictly stable processes satisfying Taylor’s condition (A). This leads naturally to a characterization of local time in terms of the corresponding Hausdorff measure function of the level set.

Mountford, Thomas Valle, Glauco
Published in
Journal of Theoretical Probability

We prove exponential convergence to equilibrium for the Fredrickson–Andersen one-spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. This was a classical conjecture related to non-attractive spin systems. Our proof relies on coupling techniques based on Harris graphical construc...

Cénac, Peggy Le Ny, Arnaud de Loynes, Basile Offret, Yoann
Published in
Journal of Theoretical Probability

We describe the scaling limits of the persistent random walks (PRWs) for which the recurrence has been characterized in Cénac et al. (J. Theor. Probab. 31(1):232–243, 2018). We highlight a phase transition phenomenon with respect to the memory: depending on the tails of the persistent time distributions, the limiting process is either Markovian or ...

Berlinkov, Artemi Järvenpää, Esa
Published in
Journal of Theoretical Probability

We study porosities in the Mandelbrot percolation process using a notion of porosity that is based on the construction geometry. We show that, almost surely at almost all points with respect to the natural measure, the construction-based mean porosities of the set and the natural measure exist and are equal to each other for all parameter values ou...

Banek, Tadeusz Zapała, August M.
Published in
Journal of Theoretical Probability

We describe the construction of a random walk in a Banach space B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {B}$$\end{document} with a quasi-orthogonal Sch...

Hajri, Hatem Arnaudon, Marc
Published in
Journal of Theoretical Probability

Inspired by Tsirelson’s proof of the non-Brownian character of Walsh Brownian motion filtration on three or more rays, we prove some results on a particular coupling of solutions to the interface stochastic differential equation on a star graph, recently introduced in Hajri and Raimond (Stoch Process Appl 126:33–65, 2016). This coupling consists of...

Sarantsev, Andrey
Published in
Journal of Theoretical Probability

Consider a finite system of Brownian particles on the real line. Each particle has drift and diffusion coefficients depending on its current rank relative to other particles, as in Karatzas et al. (Ann I H Poincare-PR 52(1):323–354, 2016). We prove some comparison results for these systems. As an example, we show that if we remove a few particles f...

Eichelsbacher, Peter Löwe, Matthias
Published in
Journal of Theoretical Probability

We apply Lindeberg’s method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random sums, in the latter situation in both the cases when the limit distribution is Gaussian or non-Gaussian. Moreo...

Le Guével, R.
Published in
Journal of Theoretical Probability

We compute the Hausdorff dimension of the image X(E) of a non-random Borel set E⊂[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E \subset [0,1]$$\end{document}, w...