Estimates on the tail probabilities of subordinators and applications to general time fractional equations

TL;DR

This paper provides estimates on the tail probabilities of subordinators and applies these results to derive bounds for solutions of general time fractional equations, including boundary value problems.

Contribution

It introduces new tail probability estimates for subordinators and applies them to analyze fundamental solutions of time fractional equations with boundary conditions.

Findings

Two-sided estimates for fundamental solutions of time fractional equations

Tail probability bounds for classes of subordinators

Applications to boundary value problems in fractional PDEs

Abstract

In this paper, we study estimates on tail probabilities $\mathbb{P}(S_r \ge t)$ of several classes of subordinators under mild assumptions on the tail of its L\'evy measure. As an application of that result, we obtain two-sided estimates for fundamental solutions of general homogeneous time fraction equations including those with Dirichlet boundary conditions.