6 papers · 1 filter
Integrals of some compound processes
Fabrizio Cinque, Enzo Orsingher
By means of the theory of compound (non-homogenoeus) Poisson processes we define a general framework which includes most of the generalizations of the Poisson processes, both in th…
Point processes of the Poisson-Skellam family
Fabrizio Cinque, Enzo Orsingher
We study a general non-homogeneous Skellam-type process with jumps of arbitrary fixed sizes. We express this process in terms of a linear combination of Poisson processes and study…
Interacting point processes
Fabrizio Cinque, Enzo Orsingher
We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their state…
Weak convergence of the integral of semi-Markov processes
Andrea Pedicone, Fabrizio Cinque
We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning…
Higher-order fractional equations and related time-changed pseudo-processes
Fabrizio Cinque, Enzo Orsingher
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to…
General Airy-type equations, heat-type equations and pseudo-processes
Fabrizio Cinque, Enzo Orsingher
We present a systematic study of higher-order Airy-type differential equations providing the explicit form of the solutions, deriving their power series expansions and a probabilis…