A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics

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dc.creatorMura, Antonio
dc.creatorMainardi, Francesco
dc.date2007-11-05
dc.date.accessioned2026-07-07T08:40:44Z
dc.date.available2026-07-07T08:40:44Z
dc.descriptionIn this paper we present a general mathematical construction that allows us to define a parametric class of $H$-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that evolves in time according to a partial integro-differential equation of fractional type. This construction is based on the theory of finite measures on functional spaces. Since the variance evolves in time as a power function, these $H$-sssi processes naturally provide models for slow and fast anomalous diffusion. Such a class includes, as particular cases, fractional Brownian motion, grey Brownian motion and Brownian motion.
dc.description14 pages, 1 figure, Presented at GF07: Linear and Non-linear Theory of Generalized Functions and Its Applications, The Banach center Bedlewo, Poland, Seprember 2-8 2007
dc.identifierhttps://arxiv.org/abs/0711.0665
dc.identifierhttp://arxiv.org/abs/0711.0665
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141457
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject26A33; 33E12; 44A10;33C60; 44A10, 45K05; 60G18
dc.titleA class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics
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