In this paper we study explicit strong solutions for two difference-differential fractional equations, defined via the generator of an immigration-death process, by using spectral methods. Moreover, we give a stochastic representation of the solutions of such difference-differential equations by means of a stable time-changed immigration-death process and we use this stochastic representation to show boundedness and then uniqueness of these strong solutions. Finally, we study the limit distribution of the time-changed process.
Fractional immigration-death processes / Ascione, G.; Leonenko, N.; Pirozzi, E.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 495:2(2021), p. 124768. [10.1016/j.jmaa.2020.124768]
Fractional immigration-death processes
Ascione G.;Pirozzi E.
2021
Abstract
In this paper we study explicit strong solutions for two difference-differential fractional equations, defined via the generator of an immigration-death process, by using spectral methods. Moreover, we give a stochastic representation of the solutions of such difference-differential equations by means of a stable time-changed immigration-death process and we use this stochastic representation to show boundedness and then uniqueness of these strong solutions. Finally, we study the limit distribution of the time-changed process.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
