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      Heavy-tailed fractional Pearson diffusions

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          Abstract

          We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

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          Limit theorems for continuous-time random walks with infinite mean waiting times

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            Models of anomalous diffusion: the subdiffusive case

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              The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes

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                Author and article information

                Journal
                2017-07-04
                Article
                10.1016/j.spa.2017.03.004
                1707.01116
                ec17297c-3f3a-47df-9c5f-c68296721430

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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