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Gamma-grey noise and gamma-grey Brownian motion

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FD2W01 - Deterministic and stochastic fractional diļ¬€erential equations and jump processes

The grey noise has been introduced for the first time by Schneider; based on it, the grey Brownian motion and the generalized  grey Brownian motion were constructed, in order to model anomalous diffusions, by mimicking the procedure for white noise and ordinary Brownian motion. These models include, as special cases, both the standard and the fractional Brownian motion. We construct and study the so-called gamma-grey noise and the gamma-grey Brownian motion, defined by means of the incomplete-gamma function (thanks to its complete monotonicity) and the Riemann-Liouville fractional derivative. Different characterizations of the process are also provided, together with the integro-differential equation satisfied by its transition density.

This talk is part of the Isaac Newton Institute Seminar Series series.

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