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Author

Enzo Orsingher

Other affiliations: University of Salerno
Bio: Enzo Orsingher is an academic researcher from Sapienza University of Rome. The author has contributed to research in topics: Brownian motion & Fractional calculus. The author has an hindex of 30, co-authored 189 publications receiving 3251 citations. Previous affiliations of Enzo Orsingher include University of Salerno.


Papers
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Journal ArticleDOI
TL;DR: In this article, a planar random motion at finite velocity performed by a particle which, at even-valued Poisson events, changes direction (each time chosen with uniform law in [0, 2π]).
Abstract: We study a planar random motion at finite velocity performed by a particle which, at even-valued Poisson events, changes direction (each time chosen with uniform law in [0, 2π]). In other words this model assumes that the time between successive deviations is a Gamma random variable. It can also be interpreted as the motion of particles that can hazardously collide with obstacles of different size, some of which are capable of deviating the motion. We obtain the explicit densities of the random position under the condition that the number of deviations N(t) is known. We express as suitable combinations of distributions of the motion described by a particle changing direction at all Poisson events. The conditional densities of and are connected by means of a new discrete-valued random variable, whose distribution is expressed in terms of Beta integrals. The technique used in the analysis is based on rather involved properties of Bessel functions, which are derived and explored in detail in order to make th...

23 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show connections between special functions arising from generalized COM-Poisson type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators.
Abstract: In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results are obtained, showing the particular role of Hadamard-type derivatives in connection with a recently introduced generalization of the Le Roy function. We are also able to prove a general connection between fractional hyper-Bessel-type equations involving Hadamard operators and Le Roy functions.

23 citations

Journal ArticleDOI
TL;DR: In this paper, the initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation.
Abstract: Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The equation of vibrations of plates is considered and the case of circular vibrating disks CR is investigated by applying the methods of planar orthogonally reflecting Brownian motion within CR. The analysis of the fractional version (of order ν) of the Fresnel equation is also performed and, in detail, some specific cases, like ν=1/2, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process F(t), t>0 with real sign-varying density is constructed and some of its properties examined. The composition of F with reflecting Brownian motion B yields the law of biquadratic heat equation while the composition of F with the first passage time Tt of B produces a genuine probability law strictly connected with the Cauchy process.

22 citations

Journal ArticleDOI
TL;DR: In this paper, the exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined) and the absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed.
Abstract: The exact distribution of a cyclic planar motion with three directions is explicitly derived in terms of Bessel functions of order three (suitably combined). The absolutely continuous part of the distribution is proved to satisfy suitable boundary conditions and some of its properties are analyzed. The transformations converting the governing equations of order three is presented and its solutions (used here) derived by applying the Frobenius method.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce non-decreasing jump processes with independent and time non-homogeneous increments, which generalize subordinators in the sense that their Laplace exponents are possibly different Bernstein functions for each time t. Although they are not Levy processes, they somehow generalise subordinators, and by means of these processes, a generalization of subordinate semigroups, a two-parameter semigroup (propagators) arise and a Phillips formula which leads to time dependent generators.
Abstract: In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not Levy processes, they somehow generalize subordinators in the sense that their Laplace exponents are possibly different Bernstein functions for each time t. By means of these processes, a generalization of subordinate semigroups in the sense of Bochner is proposed. Because of time-inhomogeneity, two-parameter semigroups (propagators) arise and we provide a Phillips formula which leads to time dependent generators. The inverse processes are also investigated and the corresponding governing equations obtained in the form of generalized variable order fractional equations. An application to a generalized subordinate Brownian motion is also examined.

21 citations


Cited by
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Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

01 Jan 2016
TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

4,085 citations

Book ChapterDOI
01 Jan 2015

3,828 citations

Book
01 Jan 2013
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

1,957 citations