A noise reinforced Brownian motion is a centered Gaussian process B ̂=(B ̂ (t)) t≥ 0 ̂
B=(̂ B (t)) _ t ≧ 0 with covariance 𝔼 (B ̂ (t) B ̂ (s))=(1− 2 p)− 1 tps 1− p for 0≤ s≤ …

Abstract Let X_1, X_2, ... X 1, X 2,… be iid copies of some real random variable X. For any
deterministic ε _2, ε _3, ... ε 2, ε 3,… in {0, 1\} 0, 1, a basic algorithm introduced by HA Simon …

The motivation for this paper is the study of the phase transition for recurrence/transience of
a class of self‐interacting random walks on trees, which includes the once‐reinforced …

Random walks on dynamic graphs have received increasingly more attention from different
academic communities over the last decade. Despite the relatively large literature, little is …

We study the asymptotic behaviour of once-reinforced biased random walk (ORbRW) on
Galton-Watson trees. Here the underlying (unreinforced) random walk has a bias towards or …

This paper is devoted to the study of the so-called WARM reinforcement models that are
generalisations of Pólya's urn. We show that in the graph setting, once the exponent α of the …

The branching-ruin number of a tree, which describes its asymptotic growth and geometry,
can be seen as a polynomial version of the branching number. This quantity was defined by …

We study a stochastic geometric flow that describes a growing submanifold $\mathbb
{M}(t)\subseteq\mathbb {R}^{\mathrm {d}+ 1} $. It is an SPDE that comes from a continuum …

In this paper, we focus on studying the long time behaviors of a type of random walk called
the $\delta $ once-reinforced random walk ($\delta $-ORRW) on a finite connected graph …

Vladas was born in Vilnius, Lithuania, on August 23, 1963, and did his undergraduate
studies in Mathematics from 1982 to 1985 at Vilnius University. There, in 1986, he received …