Censored fractional Bernstein derivatives and stochastic processes

Abstract

In this paper, we define the censored fractional Bernstein derivative on the positive half line (0, ∞) based on the Bernstein Riemann--Liouville fractional derivative. This derivative can be shown to be the generator of the censored subordinator by solving a resolvent equation. We also show that the censored subordinator hits the boundary in finite time under certain conditions.

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