arXiv subjects

Cailing Li

Publications and source records attributed to Cailing Li.

3 recordsLinked to original sources

arXiv2025

Bernstein Fractional Derivatives: Censoring and Stochastic Processes

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 $S^c = (S_t^c)_{t\geq 0}$, which is obtained either via a pathwise construction by removing those jumps from the decreasing subordinator $(x-S_t)_{t\geq 0}$, $x>0$, that drive the path into negative territory, or via 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 $S^c$.

math.PR↗

arXiv2024

Censored fractional Bernstein derivatives and stochastic processes

In this paper, we define the censored fractional Bernstein derivative on the positive half line $(0, \infty)$ 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.

math.PR↗

arXiv2024

The mapping properties of fractional derivatives in weighted fractional Sobolev space

We study the mapping behavior of the Marchaud fractional derivative with different extensions in the scale of fractional weighted Sobolev spaces. In particular we show that the $\alpha$--order Riemann--Liouville fractional derivative maps $W^{p,s}_0(\Omega)$ to $W^{p,s-\alpha}(\Omega)$, for all $0<\alpha<s<1$ and the $\alpha$--order Marchaud fractional derivative with even extension maps the fractional Sobolev space $W^{p,s}((0,\infty))$ to $W^{p,s-\alpha}(\real)$ for all $0<\alpha<s<1$ and $ps\geq1$ . The proof is based on the Calder\'{o}n--Lions interpolation theorem.

math.CA↗