Year: 2025
Type: article
Abstract: We define censored fractional Bernstein derivatives on the positive half-line based on the Bernstein–Riemann–Liouville fractional derivative. The censored fractional derivative turns out to be the generator of the censored decreasing subordinator $$S^c = (S_t^c)_{t\geqslant 0}$$ S c = ( S t c ) t ⩾ 0 . We provide two constructions of the censored subordinator: (i) pathwise by removing those jumps from the decreasing subordinator $$(x-S_t)_{t\geqslant 0}$$ ( x - S t ) t ⩾ 0 , $$x>0$$ x > 0 , that drive the path into negative territory. (ii) via a semigroup approach and the Hille–Yosida theorem. Then we show that the censored decreasing subordinator has only finite life-time, and we identify various probability distributions related to $$S^c.$$ S c .
Authors: David Berger, Cailing Li, René L. Schilling
Institution: Technische Universität Dresden
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,590
OpenAlex ID: W4417442000