IRIS Uni Torinohttps://iris.unito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sat, 14 Dec 2019 06:47:04 GMT2019-12-14T06:47:04Z10401The space-fractional Poisson processhttp://hdl.handle.net/2318/92228Titolo: The space-fractional Poisson process
Abstract: In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t\ge 0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k^\alpha (t) = -\lambda^\alpha (1-B)^\alpha p_k^\alpha(t)$, where $(1-B)^\alpha$ is the fractional difference operator found in time series analysis.
We explicitly obtain the distributions $p_k^\alpha(t)$, the probability generating
functions $G_\alpha(u,t)$, which are also expressed as distributions of the minimum of i.i.d.\ uniform random variables.
The comparison with the time-fractional Poisson process is investigated and finally, we arrive at the more general space-time-fractional Poisson process of which we give the explicit distribution.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2318/922282012-01-01T00:00:00ZAnalysis of Metal Cutting Acoustic Emission by Time Series Modelshttp://hdl.handle.net/2318/93347Titolo: Analysis of Metal Cutting Acoustic Emission by Time Series Models
Abstract: We analyse some acoustic emission time series obtained from a lathe machining process. Considering the dynamic evolution of the process we apply two classes of well known stationary stochastic time series models. We apply a preliminary root mean square (RMS) transformation followed by an ARMA analysis; results thereof are mainly related to the description of the continuous part (plastic deformation) of the signal. An analysis of acoustic emission, as some previous works show, may also be performed with the scope of understanding the evolution of the ageing process that causes the degradation of the working tools. Once the importance of the discrete part of the acoustic emission signals (i.e. isolated amplitude bursts) in the ageing process is understood, we apply a stochastic analysis based on point processes waiting times between bursts and to identify a parameter with which to characterise the wear level of the working tool. A Weibull distribution seems to adequately describe the waiting times distribution.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/2318/933472010-01-01T00:00:00ZSuperprocesses as models for information dissemination in the Future Internethttp://hdl.handle.net/2318/142061Titolo: Superprocesses as models for information dissemination in the Future Internet
Abstract: Future Internet will be composed by a tremendous number of potentially interconnected people and
devices, offering a variety of services, applications and communication opportunities.
In particular, short-range wireless communications, which are available on almost all portable devices,
will enable the formation of the largest cloud of interconnected, smart computing devices mankind has ever
dreamed about: the Proximate Internet.
In this paper, we consider superprocesses, more specifically super Brownian motion, as a suitable
mathematical model to analyse a basic problem of information dissemination arising in the
context of Proximate Internet. The proposed model provides a promising analytical framework to both
study theoretical properties related to the information dissemination process and to devise efficient
and reliable simulation schemes for very large systems.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2318/1420612014-01-01T00:00:00ZTransient behavior of fractional queues and related processeshttp://hdl.handle.net/2318/144359Titolo: Transient behavior of fractional queues and related processes
Abstract: We propose a generalization of the classical M/M/1 queue process. The resulting
model is derived by applying fractional derivative operators to a system of difference-
differential equations. This generalization includes both non-Markovian and Markovian
properties which naturally provide greater flexibility in modeling real queue systems than
its classical counterpart. Algorithms to simulate M/M/1 queue process and the related linear
birth-death process are provided. Closed-form expressions of the point and interval estimators of the parameters of the proposed fractional stochastic models are also presented. These
methods are necessary to make these models usable in practice. The proposed fractional
M/M/1 queue model and the statistical methods are illustrated using financial data.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2318/1443592015-01-01T00:00:00ZFractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applicationshttp://hdl.handle.net/2318/151470Titolo: Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications
Abstract: In this paper we discuss some explicit results
related to the fractional Klein--Gordon equation involving fractional
powers of the D'Alembert operator. By means of a space-time transformation,
we reduce the fractional Klein--Gordon equation to a case of
fractional hyper-Bessel equation. We find an explicit
analytical
solution by using the McBride theory of fractional powers of hyper-Bessel operators.
These solutions are expressed in terms of multi-index
Mittag-Leffler functions studied by Kiryakova and Luchko.
A discussion of these results within the framework of
linear dispersive wave equations is provided. We also
present exact solutions of the fractional Klein--Gordon equation in the higher dimensional cases.
Finally, we suggest a method of finding travelling wave
solutions of the nonlinear fractional Klein--Gordon equation
with power law nonlinearities.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2318/1514702014-01-01T00:00:00ZAnalytic solutions of fractional differential equations by operational methodshttp://hdl.handle.net/2318/103772Titolo: Analytic solutions of fractional differential equations by operational methods
Abstract: We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation of differential equations of mathematical physics. Fractionality is obtained by substituting the ordinary integer-order derivative with the Caputo fractional derivative. Furthermore, operational relations between ordinary and fractional differentiation are shown and discussed in detail. Finally, a last example concerns the application of the method to the study of a fractional Poisson process.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2318/1037722012-01-01T00:00:00ZDiscussion on the paper "On Simulation and Properties of the Stable Law by L. Devroye and L. James"http://hdl.handle.net/2318/152706Titolo: Discussion on the paper "On Simulation and Properties of the Stable Law by L. Devroye and L. James"
Abstract: We congratulate the authors for the interesting paper. The reading has been really pleasant and instructive. We discuss briefly only some of the interesting results given in [6] with particular attention to evolution problems. The contribution of the results collected in the paper is useful in a more wide class of applications in many areas of applied mathematics.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2318/1527062014-01-01T00:00:00ZFractional calculus modelling for unsteady unidirectional flow of incompressible fluids with time-dependent viscosityhttp://hdl.handle.net/2318/103197Titolo: Fractional calculus modelling for unsteady unidirectional flow of incompressible fluids with time-dependent viscosity
Abstract: In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the time dependent viscosity by using an integro-differential term and therefore generalizing the classical equation of a Newtonian viscous fluid. A possible useful choice, in this framework, is to use a rheology based on stress/strain relation generalized by fractional calculus modelling. This is a model that can be used in applied problems, taking into account a power law time variability of the viscosity coefficient. We find analytic solutions of initial value problems in an unbounded and bounded domain. Furthermore, we discuss the explicit solution in a meaningful particular case.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2318/1031972012-01-01T00:00:00ZHilfer-Prabhakar Derivatives and Some Applicationshttp://hdl.handle.net/2318/144360Titolo: Hilfer-Prabhakar Derivatives and Some Applications
Abstract: We present a generalization of Hilfer derivatives in which Riemann-Liouville integrals are replaced by
more general Prabhakar integrals. We analyze and discuss its properties. Furthermore, we show some
applications of these generalized Hilfer-Prabhakar derivatives in classical equations of mathematical
physics such as the heat and the free electron laser equations, and in difference-differential equations
governing the dynamics of generalized renewal stochastic processes.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2318/1443602014-01-01T00:00:00ZRandomly Stopped Nonlinear Fractional Birth Processeshttp://hdl.handle.net/2318/117871Titolo: Randomly Stopped Nonlinear Fractional Birth Processes
Abstract: We present and analyse the nonlinear classical pure birth process $\mathpzc{N} (t)$, $t>0$,
and the fractional pure birth process $\mathpzc{N}^\nu (t)$, $t>0$, subordinated to
various random times.
We derive the state probability distribution $\hat{p}_k (t)$,
$k \geq 1$ and, in some cases, we also present the corresponding governing
differential equation.
Various types of compositions of the fractional pure birth process $\mathpzc{N}^\nu(t)$
have been examined in the second part of the paper. In particular, the processes
$\mathpzc{N}^\nu(T_t)$, $\mathpzc{N}^\nu(\mathpzc{S}^\alpha(t))$, $\mathpzc{N}^\nu(T_{2\nu}(t))$,
have been analysed, where
$T_{2\nu}(t)$, $t>0$, is a process related to fractional diffusion equations.
As a byproduct
of our analysis, some formulae relating Mittag--Leffler functions are obtained.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/2318/1178712013-01-01T00:00:00Z