29 citations · 187 across the 39 of their papers we have counts for
35 papers · 1 filter
On the Laplace equation with non-local dynamical boundary conditions
Raffaela Capitanelli, Mirko D'Ovidio
Aim of the paper is to study non-local dynamic boundary conditions of reactive-diffusive type for the Laplace equation from analytic and probabilistic point of view. In particular,…
Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs
Stefano Bonaccorsi, Fausto Colantoni, Mirko D'Ovidio +1
We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random time…
Fractional Boundary Value Problems and elastic sticky Brownian motions, II: Non-local dynamic boundary conditions on smooth domains
Mirko D'Ovidio
We introduce a wide class of sticky Brownian motions (not necessarily Markovian) and study their boundary occupation time through different notions of holding times. This class con…
On the inverse gamma subordinator
Fausto Colantoni, Mirko D'Ovidio
In this paper we deal with some open problems concerned with gamma subordinators. In particular, we provide a representation for the moments of the inverse gamma subordinator. Then…
Elastic drifted Brownian motions and non-local boundary conditions
Mirko D'Ovidio, Francesco Iafrate
We provide a deep connection between elastic drifted Brownian motions and inverses to tempered subordinators. Based on this connection, we establish a link between multiplicative f…
Fractional boundary value problems
Mirko D'Ovidio
We study some functionals associated with a process driven by a fractional boundary value problem (FBVP for short). By FBVP we mean a Cauchy problem with boundary condition written…
Models of space-time random fields on the sphere
Mirko D'Ovidio, Enzo Orsingher, Lyudmyla Sakhno
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymp…
Non-local logistic equations from the probability viewpoint
Mirko D'Ovidio
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We prov…
Fractional Cauchy problem on random snowflakes
Raffaela Capitanelli, Mirko D'Ovidio
We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study…
Delayed and rushed motions through time change
Raffaela Capitanelli, Mirko D'Ovidio
We introduce a definition of delayed and rushed processes in terms of lifetimes of base processes and time-changed base processes. Then, we consider time changes given by subordina…
Drifted Brownian motions governed by fractional tempered derivatives
Mirko D'Ovidio, Francesco Iafrate, Enzo Orsingher
Fractional equations governing the distribution of reflecting drifted Brownian motions are presented. The equations are expressed in terms of tempered Riemann--Liouville type deriv…
Fractional equations via convergence of forms
Raffaela Capitanelli, Mirko D'Ovidio
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are o…
Probabilistic representation formula for the solution of fractional high order heat-type equations
Stefano Bonaccorsi, Mirko D'Ovidio, Sonia Mazzucchi
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random…
Asymptotics for time-changed diffusions
Raffaela Capitanelli, Mirko D'Ovidio
We consider time-changed diffusions driven by generators with discontinuous coefficients. The PDE's connections are investigated and in particular some results on the asymptotic an…
Spectral functions related to some fractional stochastic differential equations
Mirko D'Ovidio, Enzo Orsingher, Ludmila Sakhno
In this paper we consider fractional higher-order stochastic differential equations of the form \begin{align*} \left( μ+ c_α\frac{d^α}{d(-t)^α} \right)^βX(t) = \mathcal{E}(t) , \qu…
Skew Brownian diffusions across Koch interfaces
Raffaela Capitanelli, Mirko D'Ovidio
We consider planar skew Brownian motion (BM) across pre-fractal Koch interfaces and moving on . We study the asymptotic beh…
Fractional spherical random fields
Mirko D'Ovidio, Nikolai Leonenko, Enzo Orsingher
In this paper we study the solutions of different forms of fractional equations on the unit sphere possessing the structure of time-de…
Discussion on the paper "On Simulation and Properties of the Stable Law" by L. Devroye and L. James
Mirko D'Ovidio, Federico Polito
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 Devroy…
Fractional Poisson process with random drift
Luisa Beghin, Mirko D'Ovidio
We study the connection between PDEs and Lévy processes running with clocks given by time-changed Poisson processes with stochastic drifts. The random times we deal with are theref…
Coordinate changed random fields on manifolds
Mirko D'Ovidio, Erkan Nane
We introduce a class of time dependent random fields on compact Riemannian monifolds. These are represented by time-changed Brownian motions. These processes are time-changed diffu…
Fractional Diffusion-Telegraph Equations and their Associated Stochastic Solutions
Mirko D'Ovidio, Federico Polito
We present the stochastic solution to a generalized fractional partial differential equation involving a regularized operator related to the so-called Prabhakar operator and admitt…
Coordinates changed random fields on the sphere
Mirko D'Ovidio
We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields…
Continuous random walks and fractional powers of operators
Mirko D'Ovidio
We derive a probabilistic representation for the Fourier symbols of the generators of some stable processes.
Time-changed processes governed by space-time fractional telegraph equations
Mirko D'Ovidio, Enzo Orsingher, Bruno Toaldo
In this work we construct compositions of processes of the form \bm{S}_n^{2β}(c^2 \mathpzc{L}^ν(t) \r, t>0, ν\in (0, 1/2], β\in (0,1], n \in \mathbb{N}, whose distribution is relat…