| Título: | The Fractional Poisson Process and the Inverse Stable Subordinator |
| Autores: |
Meerschaert, Mark M; Michigan State University Nane, Erkan; Auburn University Vellaisamy, P.; Indian Institute of Technology Bombay |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Fractional Poisson process; Inverse stable subordinator; Renewal process; Mittag-Leffler waiting time; Fractional difference-differential equations; Caputo fractional derivative; Generalized Mittag-leffler function; Continuous time random walk limit; Di 60K05; 33E12; 26A33 |
| Descripción: | The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extends to a broad class of renewal processes that include models for tempered fractional diffusion, and distributed-order (e.g., ultraslow) fractional diffusion. The paper also {discusses the relation between} the fractional Poisson process and Brownian time. |
| Idioma: | No aplica |
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