scholarly journals Tempered relaxation equation and related generalized stable processes

2020 ◽  
Vol 23 (5) ◽  
pp. 1248-1273
Author(s):  
Luisa Beghin ◽  
Janusz Gajda
Keyword(s):  
Dependence Structure ◽  
Relaxation Equation ◽  
Temporal Dependence ◽  
Stable Law ◽  
Stable Case ◽  
New Class ◽  
Relaxation Functions ◽  
Local Deviation ◽  
Fractional Relaxation ◽  
Special Case

Abstract Fractional relaxation equations, as well as relaxation functions time-changed by independent stochastic processes have been widely studied (see, for example, [21], [33] and [11]). We start here by proving that the upper-incomplete Gamma function satisfies the tempered-relaxation equation (of index ρ ∈ (0, 1)); thanks to this explicit form of the solution, we can then derive its spectral distribution, which extends the stable law. Accordingly, we define a new class of selfsimilar processes (by means of the n-times Laplace transform of its density) which is indexed by the parameter ρ: in the special case where ρ = 1, it reduces to the stable subordinator. Therefore the parameter ρ can be seen as a measure of the local deviation from the temporal dependence structure displayed in the standard stable case.

Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Akbar Zada
Keyword(s):  
Fractional Derivative ◽  
Positive Solutions ◽  
Caputo Fractional Derivative ◽  
Existence And Uniqueness ◽  
Relaxation Equation ◽  
Monotone Iterative ◽  
Banach Contraction ◽  
Uniqueness Of The Solution ◽  
Fractional Relaxation ◽  
The Banach Contraction Principle

Abstract This manuscript is committed to deal with the existence and uniqueness of positive solutions for fractional relaxation equation involving ψ-Caputo fractional derivative. The existence of solution is carried out with the help of Schauder’s fixed point theorem, while the uniqueness of the solution is obtained by applying the Banach contraction principle, along with Bielecki type norm. Moreover, two explicit monotone iterative sequences are constructed for the approximation of the extreme positive solutions to the proposed problem. Lastly, two examples are presented to support the obtained results.

ON A MULTIVARIATE GENERALIZED POLYA PROCESS WITHOUT REGULARITY PROPERTY

2019 ◽  
Vol 34 (4) ◽  
pp. 484-506
Author(s):  
Ji Hwan Cha ◽  
F.G. Badía
Keyword(s):  
Regularity Property ◽  
Dependence Structure ◽  
Counting Processes ◽  
Multiple Events ◽  
New Class ◽  
Different Types ◽  
Polya Process ◽  
Multivariate Dependence ◽  
Pólya Process ◽  
Stochastic Properties

Most of the multivariate counting processes studied in the literature are regular processes, which implies, ignoring the types of the events, the non-occurrence of multiple events. However, in practice, several different types of events may occur simultaneously. In this paper, a new class of multivariate counting processes which allow simultaneous occurrences of multiple types of events is suggested and its stochastic properties are studied. For the modeling of such kind of process, we rely on the tool of superposition of seed counting processes. It will be shown that the stochastic properties of the proposed class of multivariate counting processes are explicitly expressed. Furthermore, the marginal processes are also explicitly obtained. We analyze the multivariate dependence structure of the proposed class of counting processes.

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

scholarly journals On the ergodic distribution of oscillating queueing systems

2003 ◽  
Vol 16 (4) ◽  
pp. 311-326 ◽  
Author(s):  
Mykola Bratiychuk ◽  
Andrzej Chydzinski
Keyword(s):  
Queueing Systems ◽  
Numerical Example ◽  
New Class ◽  
Ergodic Distribution ◽  
Number Of Customers ◽  
Special Case

This paper examines a new class of queueing systems and proves a theorem on the existence of the ergodic distribution of the number of customers in such a system. An ergodic distribution is computed explicitly for the special case of a G/M−M/1 system, where the interarrival distribution does not change and both service distributions are exponential. A numerical example is also given.

scholarly journals Sum of Bernoulli Mixtures: Beyond Conditional Independence

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Taehan Bae ◽  
Ian Iscoe
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Random Variable ◽  
Dependence Structure ◽  
Sample Distribution ◽  
Mixing Distribution ◽  
Bernoulli Random Variables ◽  
New Class ◽  
Bernoulli Mixtures ◽  
Conditional Tail Expectation

We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we calldouble mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.

scholarly journals The Inverse Lomax-G Family with application to Breaking Strength Data

2020 ◽  
pp. 49-60
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Breaking Strength ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Strength Data ◽  
New Class ◽  
Class A ◽  
New Family ◽  
Competing Models ◽  
Special Case ◽  
Study Application

We proposed a new class of distributions with two additional positive parameters called the Inverse Lomax-G (IL-G) class. A special case was discussed, by taking Weibull as a baseline. Different properties of the new family that hold for any type of baseline model are derived including moments, moment generating function, entropy for Renyi, entropy for Shanon, and order statistics. The performances of the maximum likelihood estimates of the parameters of the sub-model of the Inverse Lomax-G family were evaluated through a simulation study. Application of the sub-model to the Breaking strength data clearly showed its superiority overthe other competing models.

scholarly journals Weighted proportional mean inactivity time model

2021 ◽  
Vol 7 (3) ◽  
pp. 4038-4060
Author(s):  
Mohamed Kayid ◽  
◽  
Adel Alrasheedi
Keyword(s):  
Frailty Model ◽  
Real Data ◽  
Survival Models ◽  
Dependence Structure ◽  
Time Model ◽  
Data Set ◽  
Population Variable ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Special Case

<abstract><p>In this paper, a mean inactivity time frailty model is considered. Examples are given to calculate the mean inactivity time for several reputable survival models. The dependence structure between the population variable and the frailty variable is characterized. The classical weighted proportional mean inactivity time model is considered as a special case. We prove that several well-known stochastic orderings between two frailties are preserved for the response variables under the weighted proportional mean inactivity time model. We apply this model on a real data set and also perform a simulation study to examine the accuracy of the model.</p></abstract>

scholarly journals Global Analysis and the Periodic Character of a Class of Difference Equations

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 131 ◽  
Author(s):  
George E. Chatzarakis ◽  
Elmetwally M. Elabbasy ◽  
Osama Moaaz ◽  
Hamida Mahjoub
Keyword(s):  
Mathematical Models ◽  
Difference Equations ◽  
Global Analysis ◽  
New Class ◽  
Special Case ◽  
Life Phenomenon

In biology, Difference equations is often used to understand and describe life phenomenon through mathematical models. So, In this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case.

Sign in / Sign up

Export Citation Format

Share Document