98 citations · 185 across the 19 of their papers we have counts for
23 papers · 1 filter
Monte Carlo Approximations of Time-Nonlocal Diffusions in Bounded Domains
Ivan Biočić, Daniel E. Cedeño-Girón, Aleksandar Mijatović +1
We develop and analyze a Monte Carlo method for sampling killed anomalous diffusions obtained by time-changing Brownian motion with drift by the inverse of a subordinator. The meth…
Modelling Anomalous Diffusion: The Role of CTRWs and Non-Local Dynamics
Ivan Biočić, Bruno Toaldo
These notes provide a self-consistent summary of the stochastic approach to anomalous diffusion based on Continuous Time Random Walks (CTRWs) and their scaling limits. An introduct…
Random Flights and Anomalous Diffusion: A Non-Markovian Take on Lorentz Processes
Lorenzo Facciaroni, Costantino Ricciuti, Enrico Scalas +1
We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Galla…
Para-Markov chains and related non-local equations
Lorenzo Facciaroni, Costantino Ricciuti, Enrico Scalas +1
There is a well established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by def…
Time-changed Markov processes and space-time coupled non-local equations
Giacomo Ascione, Enrico Scalas, Bruno Toaldo +1
In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of t…
Regularity and asymptotics of densities of inverse subordinators
Giacomo Ascione, Mladen Savov, Bruno Toaldo
In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the lit…
Non-local heat equations with moving boundary
Giacomo Ascione, Pierre Patie, Bruno Toaldo
In this paper we consider non-local (in time) heat equations on time-increasing parabolic sets whose boundary is determined by a suitable curve. We provide a notion of solution for…
Limit theorems for prices of options written on semi-Markov processes
Enrico Scalas, Bruno Toaldo
We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type…
From semi-Markov random evolutions to scattering transport and superdiffusion
Costantino Ricciuti, Bruno Toaldo
We here study random evolutions on Banach spaces, driven by a class of semi-Markov processes. The expectation (in the sense of Bochner) of such evolutions is shown to solve some ab…
Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation
Mladen Savov, Bruno Toaldo
In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of s…
On the exit time from open sets of some semi-Markov processes
Giacomo Ascione, Enrica Pirozzi, Bruno Toaldo
In this paper we characterize the distribution of the first exit time from an arbitrary open set for a class of semi-Markov processes obtained as time-changed Markov processes. We…
Semi-Markov models and motion in heterogeneous media
Costantino Ricciuti, Bruno Toaldo
In this paper we study continuous time random walks (CTRWs) such that the holding time in each state has a distribution depending on the state itself. For such processes, we provid…
On semi-Markov processes and their Kolmogorov's integro-differential equations
Enzo Orsingher, Costantino Ricciuti, Bruno Toaldo
Semi-Markov processes are a generalization of Markov processes since the exponential distribution of time intervals is replaced with an arbitrary distribution. This paper provides…
Time-inhomogeneous jump processes and variable order operators
Enzo Orsingher, Costantino Ricciuti, Bruno Toaldo
In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not Lévy processes, they somehow generalize subordi…
Relaxation patterns and semi-Markov dynamics
Mark M. Meerschaert, Bruno Toaldo
Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variet…
Population models at stochastic times
Enzo Orsingher, Costantino Ricciuti, Bruno Toaldo
In this article, we consider time-changed models of population evolution , where is a counting process and is a subordinat…
Lévy mixing related to distributed order calculus, subordinators and slow diffusions
Bruno Toaldo
The study of distributed order calculus usually concerns about fractional derivatives of the form for some measure , eventually a probability mea…
Counting processes with Bernštein intertimes and random jumps
Enzo Orsingher, Bruno Toaldo
We consider here point processes , , with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernštein functions with Lévy…
Convolution-type derivatives, hitting-times of subordinators and time-changed -semigroups
Bruno Toaldo
In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by me…
Pseudoprocesses related to space-fractional higher-order heat-type equations
Enzo Orsingher, Bruno Toaldo
In this paper we construct pseudo random walks (symmetric and asymmetric) which converge in law to compositions of pseudoprocesses stopped at stable subordinators. We find the high…
Even-order pseudoprocesses on a circle and related Poisson kernels
Enzo Orsingher, Bruno Toaldo
Pseudoprocesses, constructed by means of the solutions of higher-order heat-type equations have been developed by several authors and many related functionals have been analyzed by…
Space-time fractional equations and the related stable processes at random time
Enzo Orsingher, Bruno Toaldo
In this paper we consider the general fractional equation \sum_{j=1}^m λ_j \frac{\partial^{ν_j}}{\partial t^{ν_j}} w(x_1,..., x_n ; t) = -c^2 (-Δ)^βw(x_1,..., x_n ; t), for ν_j \in…
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…