Heavy-tailed fractional Pearson diffusions (CROSBI ID 243954)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Leonenko, Nikolai ; Papić, Ivan ; Sikorskii, Alla ; Šuvak, Nenad
engleski
Heavy-tailed fractional Pearson diffusions
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.
Fractional diffusion ; Fractional backward Kolmogorov equation ; Hypergeometric function ; Mittag-Leffler function ; Pearson diffusion ; Spectral representation ; Transition density ; Whittaker function
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Podaci o izdanju
127 (11)
2017.
3512-3535
objavljeno
0304-4149
1879-209X
10.1016/j.spa.2017.03.004