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Mirko D'Ovidio

Bio: Mirko D'Ovidio is an academic researcher from Sapienza University of Rome. The author has contributed to research in topics: Fractional calculus & Brownian motion. The author has an hindex of 14, co-authored 76 publications receiving 560 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors construct compositions of vector processes of the form, t > 0,, β ∈ (0, 1),, whose distribution is related to space-time fractional n-dimensional telegraph equations.
Abstract: In this work, we construct compositions of vector processes of the form , t > 0, , β ∈ (0, 1], , whose distribution is related to space-time fractional n-dimensional telegraph equations. We present within a unifying framework the pde connections of n-dimensional isotropic stable processes S2βn whose random time is represented by the inverse , t > 0, of the superposition of independent positively skewed stable processes, , t > 0, (H2ν1, Hν2, independent stable subordinators). As special cases for n = 1, and β = 1, we examine the telegraph process T at Brownian time B ([14]) and establish the equality in distribution , t > 0. Furthermore the iterated Brownian motion ([2]) and the two-dimensional motion at finite velocity with a random time are investigated. For all these processes, we present their counterparts as Brownian motion at delayed stable-distributed time.

55 citations

Journal ArticleDOI
TL;DR: In this article, the explicit representation of solutions to fractional and anomalous diffusions related to Sturm-Liouville problems of fractional order associated with fractional power function spaces is studied.

38 citations

Journal ArticleDOI
TL;DR: In this article, the transition laws of stable subordinators and their inverse processes are expressed by means of transition laws for fractional higher-order equations and the explicit solutions of these transition laws are presented.

34 citations

Posted Content
TL;DR: In this paper, the explicit representation of solutions to fractional and anomalous diffusions related to Sturm-Liouville problems of fractional order associated with fractional power function spaces is discussed.
Abstract: Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the explicit laws of certain stable processes turn out to be fundamental. This paper directs one's efforts towards the explicit representation of solutions to fractional and anomalous diffusions related to Sturm-Liouville problems of fractional order associated to fractional power function spaces. Furthermore, we study a new version of the Bochner's subordination rule and we establish some connections between subordination and space-fractional operator

33 citations

Journal ArticleDOI
TL;DR: In this paper, the stochastic solution to a generalized fractional partial differential equation (fPDE) involving a regularized operator related to the so-called Prabhakar operator was presented.
Abstract: We present the stochastic solution to a generalized fractional partial differential equation (fPDE) involving a regularized operator related to the so-called Prabhakar operator and admitting as spe...

31 citations


Cited by
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Book ChapterDOI
01 Jan 2015

3,828 citations

Journal ArticleDOI
TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.
Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

3,647 citations

Journal ArticleDOI
TL;DR: A generalization of Hilfer derivatives in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals is presented, which shows some applications in classical equations of mathematical physics such as the heat and the free electron laser equations.

196 citations