The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes
The leading role of a special function of the Wright-type, referred to as M-Wright or Mainardi function, within a parametric class of self-similar stochastic processes with stationary increments, is surveyed. This class of processes, known as generalized grey Brownian motion, provides models for bot...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/647 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/647 |
| Access Level: | acceso abierto |
| Palabra clave: | Erdélyi-Kober fractional diffusion fractional diffusion generalized grey Brownian motion M-Wright function |
| Sumario: | The leading role of a special function of the Wright-type, referred to as M-Wright or Mainardi function, within a parametric class of self-similar stochastic processes with stationary increments, is surveyed. This class of processes, known as generalized grey Brownian motion, provides models for both fast and slow anomalous diffusion. In view of a subordination-type formula involving M-Wright functions, these processes emerge to have all finite moments and be uniquely defined by their mean and auto-covariance structure like Gaussian processes. The corresponding master equation is shown to be a fractional differential equation in the Erdélyi-Kober sense and the diffusive process is named Erdélyi-Kober fractional diffusion. In Appendix, an historical overview on the M-Wright function is reported. |
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