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On Ikehara type Tauberian theorems with $$O(x^\gamma )$$ O ( x γ ) remainders

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2017
Motivated by analytic number theory, we explore remainder versions of Ikehara's Tauberian theorem yielding power law remainder terms. More precisely, for $f:[1,\infty)\rightarrow{\mathbb R}$ non-negative and non-decreasing we prove $f(x)-x=O(x^\gamma)$ with ...
openaire +3 more sources

On Transient Queue-Size Distribution in a Model of WSN Node with Threshold-Type Power-Saving Algorithm. [PDF]

Sensors (Basel), 2022
Kempa WM, Kurzyk D.
europepmc +1 more source

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium [PDF]

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only ...
Howell, D. R. +3 more
core +1 more source

Small deviations in p-variation for stable processes

, 2003
Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and $\k = \k (\alpha, p)\in (0, +\infty)$ such that $$\lim_{\ee\downarrow 0}\ee ...
Simon, T.
core +1 more source

Spherically Restricted Random Hyperbolic Diffusion. [PDF]