Drifted Brownian motions governed by fractional tempered derivatives

Mirko D'Ovidio, Francesco Iafrate, Enzo Orsingher
2018 Modern Stochastics: Theory and Applications  
Fractional equations governing the distribution of reflecting drifted Brownian motions are presented. The equations are expressed in terms of tempered Riemann--Liouville type derivatives. For these operators a Marchaud-type form is obtained and a Riesz tempered fractional derivative is examined, together with its Fourier transform.
doi:10.15559/18-vmsta114 fatcat:6f24cjph7nhh5jaymxac3ci2mq