We establish empirical quantile process CLTs based on n independent copies of a stochastic process {Xt : t ∈ E} that are uniform in t ∈ E and quantile levels α ∈ I, where I is a closed subinterval of (0, 1). Typically E = [0, T ], or a finite product of such intervals. Also included are CLT’s for the empirical process based on {IXt≤y − Pr(Xt ≤ y) : t ∈ E, y ∈ R} that are uniform in t ∈ E, y ∈ R...

Many random phenomena in the environmental and geophysical sciences are functions of both space and time; these are usually called spatio-temporal processes. Typically, the spatio-temporal process is observed over discrete equidistant time and at irregularly spaced locations in space. One important aim is to develop statistical models based on what is observed. While doing so a commonly used as...

Time series measured from real spatially extended systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to detect spatial coherent patterns in nonstationary multivariate time-series. In contrast with classical methods, the surrogate data used here are real...

The Master Equation approach to model anomalous diffusion is considered. Anomalous diffusion in complex media can be described as the result of a superposition mechanism reflecting inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equatio...

Abstract Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of the underlying stochastic process. Often, it can be assumed a priori that the underlying discrete-time random walk model is independent from absolu...

We consider the dynamic pricing problem of a durable good monopolist with full commitment power, when a new version of the good is expected at some point in the future. The new version of the good is superior to the existing one, bringing a higher flow utility. If the arrival is a stationary stochastic process, then the corresponding optimal price path is shown to be constant for both versions ...

Scaling refers to the absence of a particular characteristic time scale controlling a stochastic process. The literature on network traffic widely agrees on a monoscaling Gaussian self-similar traffic model at timescales larger than the round-trip time (RTT) of TCP segments. In this paper we show evidence that multiscaling may be present at these timescales. We discuss some scaling results that...

Occurrence of transactions in financial markets is known to be nicely approximated by a non-stationary Poissonian process whose mean value modulated continuously by the moving average of latest intervals [1]. This type of stochastic process is named as the self-modulated process and it is generally proved theoretically that the corresponding power spectrum is characterized by the 1/f spectrum[2...

We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently wellseparated locations are independent; it is a block-factor if it can be expressed as a finite-range function of independent variables. The problem of finding non-block-factor finitely dependent processes dates b...

In this paper we present an upper bound for the decay of correlation for the stationary stochastic process associated with the Entropy Penalized Method. Let L(x, v) : T × R → R be a C Lagrangian of the form L(x, v) = 1 2 |v| 2 − U(x) + 〈P, v〉. We point out that we do not assume more differentiability of L according the the dimension of the torus T. 1. Definitions and the set up of the problem L...