Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also pre...

We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach as in Witting (1985). Results of Aubin & Ekeland (1984) from non-smooth convex analysis are employed, along with a theorem of Komll os (1967), in order to establish the existence of a max-min optimal test and to investigate its properties. The theory is i...

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