scholarly journals Monotonicity properties for solutions of renewal equations

2021 ◽  
pp. 109226
Author(s):  
Vaios Dermitzakis ◽  
Konstadinos Politis
Keyword(s):  
Renewal Equations ◽  
Monotonicity Properties

scholarly journals Research of reliability and efficiency of technological processes of mechanical assembly production on the basis of the common semi-Markov model

2018 ◽  
Vol 224 ◽  
pp. 01138
Author(s):  
Yuri Rapatskiy ◽  
Mikhail Zamorenov ◽  
Vadim Kopp ◽  
Yuri Obzherin ◽  
Vladimir Gusev ◽  
...  
Keyword(s):  
Distribution Functions ◽  
Mechanical Assembly ◽  
Renewal Equations ◽  
Technological Processes ◽  
Threaded Connections ◽  
Proposed Model ◽  
The Common ◽  
Semi Markov Processes ◽  
Simulation Parameters ◽  
Assembly Production

In the article a common semi-Markov mathematical model is considered that allows one to investigate the productivity and reliability of various technological processes of mechanical assembly production. The proposed model allows to study, inter alia, technological processes of manufacturing parts with screw and assemblies of threaded connections. Mathematical apparatus of the research is the theory of semi-Markov processes with a common phase space, which operates with a common kind of random variables distribution functions. If the considering process in the system is a subsystem located on a higher level of hierarchy, the hierarchical model for compatibility with each other levels as output simulation parameters required distribution functions. In the proposed model, based on the decision of the Markov renewal equations depend not only on the torque characteristics, but also the distribution function of time per unit of output service according to different kinds of undervalued failures.

Some complete monotonicity properties for the -gamma function

2013 ◽  
Vol 219 (21) ◽  
pp. 10538-10547 ◽  
Author(s):  
V.B. Krasniqi ◽  
H.M. Srivastava ◽  
S.S. Dragomir
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Monotonicity Properties

Monotonicity Properties of Determinants of Special Functions

2006 ◽  
Vol 26 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Mourad E.H. Ismail ◽  
Andrea Laforgia
Keyword(s):  
Special Functions ◽  
Monotonicity Properties

Higher monotonicity properties of normalized Bessel functions

2014 ◽  
Vol 12 (05) ◽  
pp. 1461007
Author(s):  
Yongping Liu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Positive Zero ◽  
Local Maxima ◽  
Monotonicity Properties

Denote by Jν the Bessel function of the first kind of order ν and μν,k is its kth positive zero. For ν > ½, a theorem of Lorch, Muldoon and Szegö states that the sequence [Formula: see text] is decreasing, another theorem of theirs states that the sequence [Formula: see text] has higher monotonicity properties. In the present paper, we proved that when ν > ½ the sequence [Formula: see text] has higher monotonicity properties and the properties imply those of the sequence of the local maxima of the function x-ν+1|Jν-1(x)|, x ∈ (0, ∞), i.e. the sequence [Formula: see text] has higher monotonicity properties.

scholarly journals On a general class of renewal risk process: analysis of the Gerber-Shiu function

2005 ◽  
Vol 37 (03) ◽  
pp. 836-856 ◽  
Author(s):  
Shuanming Li ◽  
José Garrido
Keyword(s):  
Laplace Transform ◽  
Process Analysis ◽  
Risk Process ◽  
Expected Discounted Penalty Function ◽  
Renewal Equations ◽  
The Laplace Transform ◽  
Discounted Penalty Function ◽  
Renewal Risk ◽  
Defective Renewal Equations ◽  
Expected Discounted Penalty

We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a K n distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n ∈ N). The Laplace transform of the expected discounted penalty function at ruin is derived. This leads to a generalization of the defective renewal equations given by Willmot (1999) and Gerber and Shiu (2005). Finally, explicit results are given for rationally distributed claim severities.

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