Related papers: Intermittency of trawl processes
We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…
The intermittency phenomenon is the occurrence of very high but rare peaks, which despite their rarity influence the asymptotic behaviour of the underlying system. Mathematically this can be characterised with the asymptotics of moments. In…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over…
Fractal behavior and long-range dependence have been observed in tele-traffic measurement and characterization. In this paper we show results of application of the fractal analysis to internet traffic via various methods. Our result…
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…
In this paper, we study Ruelle's probability cascades in the framework of time-inhomogeneous fragmentation processes. We describe Ruelle's cascades mechanism exhibiting a family of measures $(\nu_t,t\in [0,1[)$ that characterizes its…
We study the scaling behaviors in the wind velocity time series collected at the atmospheric surface layer and compare them with two commonly used cascade models, the truncated stable distribution and the log-normal model. Results show that…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…
We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…
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…