Related papers: Record statistics for a discrete-time random walk …
Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a…
We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width $p$ of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general…
Forensic gait analysis can aid the investigation of crimes through comparing features of gait captured in video footage. Modelling the probative value of gait evidence requires an understanding of the variation of features of gait between…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d larger than 1), are named Dirichlet when their step lengths are distributed according to a Dirichlet law. The latter continuous…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…
We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
We consider random walks with finite second moment which drifts to $-\infty$ and have heavy tail. We focus on the events when the minimum and the final value of this walk belong to some compact set. We first specify the associated…
Mobile phone data has enabled the timely and fine-grained study human mobility. Call Detail Records, generated at call events, allow building descriptions of mobility at different resolutions and with different spatial, temporal and social…
In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space…