Fractional diffusions with time-varying coefficients
Roberto Garra“Sapienza” Università di Roma 1 Dipartimento di Scienze Statistiche, , P. le A. Moro 5, 00185 Roma, ItalyEnzo Orsingher“Sapienza” Università di Roma 1 Dipartimento di Scienze Statistiche, , P. le A. Moro 5, 00185 Roma, ItalyFederico PolitoUniversità degli Studi di Torino 2 Dipartimento di Matematica “G. Peano,” , Via Carlo Alberto 10, 10123 Torino, Italy
2015en
ABI
Abstract
This paper is concerned with the fractionalized diffusion equations governing the law of the fractional Brownian motion BH(t). We obtain solutions of these equations which are probability laws extending that of BH(t). Our analysis is based on McBride fractional operators generalizing the hyper-Bessel operators L and converting their fractional power Lα into Erdélyi–Kober fractional integrals. We study also probabilistic properties of the random variables whose distributions satisfy space-time fractional equations involving Caputo and Riesz fractional derivatives. Some results emerging from the analysis of fractional equations with time-varying coefficients have the form of distributions of time-changed random variables.
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