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The telegraph process X(t), t > 0, (Goldstein, 1951) and the geometric telegraph process S(t) = s0 exp{(μ− 12σ)t+σX(t)} with μ a known constant and σ > 0 a parameter are supposed to be observed at n+1 equidistant time points ti = i∆n, i = 0, 1, . . . , n. For both models λ, the underlying rate of the Poisson process, is a parameter to be estimated. In the… (More)

- Alessandro De Gregorio, Stefano Maria Iacus
- Computational Statistics & Data Analysis
- 2010

Abstract In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between two observed paths, the… (More)

A one dimensional diffusion process X = {Xt, 0 ≤ t ≤ T }, with drift b(x) and diffusion coefficient σ(θ, x) = √ θσ(x) known up to θ > 0, is supposed to switch volatility regime at some point t∗ ∈ (0, T ). On the basis of discrete time observations from X , the problem is the one of estimating the instant of change in the volatility structure t∗ as well as… (More)

- Alessandro De Gregorio, Stefano Maria Iacus, Ben Bassat
- 2008

also known as Shannon or Kullback-Leibler entropy. Rényi information is taken as a typical measure of complexity in the areas of physics, information theory and engineering to describe dynamical or chaotic systems (see e.g Kurths et al., 1995). Rényi information, seen as a generalization of the Shannon entropy, is used to “obtain different averaging of… (More)

- Alessandro De Gregorio, Stefano Maria Iacus
- Inf. Sci.
- 2009

We deal with a planar random flight {(X(t), Y (t)), 0 < t ≤ T } observed at n + 1 equidistant times ti = i∆n, i = 0, 1, ..., n. The aim of this paper is to estimate the unknown value of the parameter λ, the underlying rate of the Poisson process. The planar random flights are not markovian, then we use an alternative argument to derive a pseudo-maximum… (More)

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity +v or −v. The changes of direction are governed by an homogeneous Poisson process with rate λ > 0. In this paper, we… (More)

- Maria Balcerowicz-Szkutnik, Alessandro Barbiero, +29 authors Grzegorz Sitek
- 2015

Finite mixtures of probability distributions may be successfully used in the modeling of probability distributions of incomes. These distributions are typically heavy tailed and positively skewed. This article deals with the problem of determining the number of components in mixture modeling. This paper considers the likelihood of ratio-based testing of the… (More)

- Alessandro De Gregorio
- ArXiv
- 2017

If φ and ψ are two continuous real-valued functions defined on a compact topological space X and G is a subgroup of the group of all homeomorphisms of X onto itself, the natural pseudo-distance dG(φ,ψ) is defined as the infimum of L(g) = ‖φ−ψ ◦ g‖∞, as g varies in G. In this paper, we make a first step towards extending the study of this concept to the case… (More)

- Alessandro De Gregorio, Stefano Maria Iacus
- J. Multivariate Analysis
- 2013

Let Xt, t ∈ [0, T ], be a d-dimensional diffusion process solution of the following stochastic differential equation dXt = b(α,Xt)dt+σ(β,Xt)dWt, where functions b and σ are suitably regular and known up to the parameters α ∈ R and β ∈ R . The process Xt is discretely observed at times ti, such that ti − ti−1 = ∆n < ∞ for 1 ≤ i ≤ n. The asymptotic scheme… (More)