27 citations · 38 across the 6 of their papers we have counts for
7 papers
Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes II
Boris Baeumer, Mihály Kovács, Lorenzo Toniazzi
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided Lévy processes. On one hand this allows modellers to use approp…
Boundary conditions for nonlocal one-sided pseudo-differential operators and the associated stochastic processes I
Boris Baeumer, Mihály Kovács, Lorenzo Toniazzi
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided Lévy processes. On one hand this allows modellers to use approp…
Censored Stable Subordinators and Fractional Derivatives
Qiang Du, Lorenzo Toniazzi, Zirui Xu
Based on the popular Caputo fractional derivative of order in , we define the censored fractional derivative on the positive half-line . This derivative pro…
Space-time coupled evolution equations and their stochastic solutions
John Herman, Ifan Johnston, Lorenzo Toniazzi
We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of…
Stochastic representation of solution to nonlocal-in-time diffusion
Qiang Du, Lorenzo Toniazzi, Zhi Zhou
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined…
Stochastic solutions for space-time fractional evolution equations on bounded domain
Lorenzo Toniazzi
Space-time fractional evolution equations are a powerful tool to model diffusion displaying space-time heterogeneity. We prove existence, uniqueness and stochastic representation o…
Generalised Fractional Evolution Equations of Caputo Type
M. E. Hernández-Hernández, V. N. Kolokoltsov, L. Toniazzi
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obt…