Related papers: Persistence exponent for discrete-time, time-rever…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
For AR(1)-processes $X_n=\rho X_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\in\mathbb{N}}$ is an i.i.d. sequence of random variables, we study the persistence probabilities $\mathbb{P}(X_0\ge 0,\dots, X_N\ge…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting…
We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further minor conditions, we show that the asymptotic behaviour of…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center of mass persistence of a random walker to the…
We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the…
We study the long-time asymptotic behavior of the position distribution of a run-and-tumble particle (RTP) in two dimensions and show that the distribution at a time $t$ can be expressed as a perturbative series in $(\gamma t)^{-1}$, where…
We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.