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Monotonicity and complete monotonicity for continuous-time Markov chains [PDF]

Comptes Rendus- Academie des Sciences Paris Serie 2 Mecanique Physique Astronomie Fascicule B, Elsevier, 2006, 2016
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in ...
Pra, PD, Louis, PY, Minelli, I
arxiv   +9 more sources

Complete monotonicity involving some ratios of gamma functions [PDF]

Journal of Inequalities and Applications, 2017
In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic.
Zhen-Hang Yang, Shen-Zhou Zheng
doaj   +2 more sources

Short Remarks on Complete Monotonicity of Some Functions [PDF]

Mathematics, 2020
In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1
Ladislav Matejíčka
doaj   +2 more sources

Logarithmically Complete Monotonicity Properties Relating to the Gamma Function [PDF]

Abstract and Applied Analysis, 2011
We prove that the function fα,β(x)=Γβ(x+α)/xαΓ(βx) is strictly logarithmically completely monotonic on (0,∞) if (α,β)∈{( α,β):1/α≤β≤1, α≠1}∪{(α,β ...
Tie-Hong Zhao, Yu-Ming Chu, Hua Wang
doaj   +2 more sources

Complete monotonicity related to the k-polygamma functions with applications [PDF]

Advances in Difference Equations, 2019
In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
doaj   +2 more sources

A complete monotonicity property of the multiple gamma function [PDF]

Comptes Rendus. Mathématique, 2020
We consider the following functions \[ f_n(x)=1-\ln x+\frac{\ln G_n(x+1)}{x} \text{ and }g_n(x)=\frac{\@root x \of {G_n(x+1)}}{x},\; x\in (0,\infty ),\; n\in \mathbb{N}, \] where $G_n(z)=\left(\Gamma _n(z)\right)^{(-1)^{n-1}}$ and $\Gamma _n$ is the ...
Das, Sourav
doaj   +2 more sources

On some complete monotonic functions [PDF]

arXiv, 2022
Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function",we confirm among other results and disprove other one.
arxiv   +3 more sources

A Characterization of Optimal Prefix Codes [PDF]

Entropy
A property of prefix codes called strong monotonicity is introduced, and it is proven that for a given source, a prefix code is optimal if and only if it is complete and strongly monotone.
Spencer Congero, Kenneth Zeger
doaj   +2 more sources

Complete Monotonicity of Special Functions

, 2015
In this work we prove that if an entire function $f(z)$ is of order strictly less than one and it has only negative zeros, then for each nonnegative integer $k,m$ the real function $\left(-\frac{1}{x}\right)^{m}\frac{d^{k}}{dx^{k}}\left(x^{k+m}\frac{d^{m}}{dx^{m}}\left(\frac{f'(x)}{f(x)}\right)\right)$ is completely monotonic on $(0,\infty ...
R. Zhang
openaire   +4 more sources

Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function [PDF]

Demonstratio Mathematica
In this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
doaj   +2 more sources