scholarly journals Delayed Renewal Process with Uncertain Random Inter-Arrival Times

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1943
Author(s):  
Xiaoli Wang ◽  
Gang Shi ◽  
Yuhong Sheng
Keyword(s):  
Random Process ◽  
Renewal Process ◽  
Random Variable ◽  
Random Delay ◽  
Renewal Theorem ◽  
Arrival Times ◽  
Chance Distribution ◽  
Renewal Rate ◽  
First Arrival

An uncertain random variable is a tool used to research indeterminacy quantities involving randomness and uncertainty. The concepts of an ’uncertain random process’ and an ’uncertain random renewal process’ have been proposed in order to model the evolution of an uncertain random phenomena. This paper designs a new uncertain random process, called the uncertain random delayed renewal process. It is a special type of uncertain random renewal process, in which the first arrival interval is different from the subsequent arrival interval. We discuss the chance distribution of the uncertain random delayed renewal process. Furthermore, an uncertain random delay renewal theorem is derived, and the chance distribution limit of long-term expected renewal rate of the uncertain random delay renewal system is proved. Then its average uncertain random delay renewal rate is obtained, and it is proved that it is convergent in the chance distribution. Finally, we provide several examples to illustrate the consistency with the existing conclusions.

RENEWAL PROCESS FOR FUZZY VARIABLES

2007 ◽  
Vol 15 (04) ◽  
pp. 493-501 ◽  
Author(s):  
DUG HUN HONG
Keyword(s):  
Renewal Process ◽  
Renewal Theorem ◽  
Arrival Times ◽  
Fuzzy Variables ◽  
Continuity Assumption

Recently, Zhao and Liu [IJUFKS 11 (2003) 573–586] proposed a "fuzzy elementary renewal theorem" and "fuzzy renewal rewards theorem" for a renewal process in which the inter-arrival times and rewards are characterized as continuous fuzzy variables. The continuity assumption is restrictive. In this note, we prove the same results without the assumption of continuity of the inter-arrival times and rewards.

scholarly journals A Method of Predicting Risk of Natural Emergencies on Road Network

2015 ◽  
Vol 4 (2) ◽  
pp. 73-82 ◽  
Author(s):  
Трофименко ◽  
Yuri Trofimenko ◽  
Якубович ◽  
A. Yakubovich
Keyword(s):  
Random Process ◽  
Road Network ◽  
Information Technologies ◽  
Random Variable ◽  
Transportation Infrastructure ◽  
Main Difficulty ◽  
Discrete Random Variable ◽  
Emergency Situations ◽  
Environmental Surveys

The main difficulty of describing natural emergency as a random process is the large number of parameters that must be quantified. Authors suggest threating the onset of emergency as a discrete random variable; each possible implementation corresponds to the defined size of the expected damage to transportation infrastructure. The analysis of the engineering and environmental surveys via geo-information technologies identified expected probability of occurrence and scale of the annual damage for 10 types of emergency situations on long-term (up to 2030) for State Company Russian Highways road network.

II.—Asymptotic Renewal Theorems

1953 ◽  
Vol 64 (1) ◽  
pp. 9-48 ◽  
Author(s):  
Walter L. Smith
Keyword(s):  
Distribution Function ◽  
Renewal Process ◽  
Age Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Renewal Theorem ◽  
Discrete Process ◽  
Main Emphasis ◽  
Image Position ◽  
Independent And Identically Distributed

SynopsisA sequence of non-negative random variables {Xi} is called a renewal process, and if the Xi may only take values on some sequence it is termed a discrete renewal process. The greatest k such that X1 + X2 + … + Xk ≤ x(> o) is a random variable N(x) and theorems concerning N(x) are renewal theorems. This paper is concerned with the proofs of a number of renewal theorems, the main emphasis being on processes which are not discrete. It is assumed throughout that the {Xi} are independent and identically distributed.If H(x) = Ɛ{N(x)} and K(x) is the distribution function of any non-negative random variable with mean K > o, then it is shown that for the non-discrete processwhere Ɛ{Xi} need not be finite; a similar result is proved for the discrete process. This general renewal theorem leads to a number of new results concerning the non-discrete process, including a discussion of the stationary “age-distribution” of “renewals” and a discussion of the variance of N(x). Lastly, conditions are established under whichThese new conditions are much weaker than those of previous theorems by Feller, Täcklind, and Cox and Smith.

scholarly journals On the Transition Probability of a Renewal Process

1957 ◽  
Vol 11 ◽  
pp. 41-51
Author(s):  
Takeyuki Hida
Keyword(s):  
Partial Differential Equations ◽  
Markov Process ◽  
Differential Equations ◽  
Renewal Process ◽  
Present Note ◽  
Transition Probability ◽  
Random Variable ◽  
Renewal Theorem ◽  
Partial Differential ◽  
Stationary Markov Process

J. L. Doob, D. Blackwell, W. Feller and other authors have obtained several results concerning the renewal theorem. Especially Doob [1] has considered the renewal process and has showed that it becomes a stationary Markov process if we add a certain initial random variable to it. In the present note, we shall study this stationary Markov process and try to determine its transition probability by virtue of a pair of partial differential equations.The author would like to express his hearty thanks to prof. A. Amakusa who has encouraged him with kind discussions throughout the course of preparing the present note.

scholarly journals Random additions in urns of integers

2021 ◽  
Vol 58 (2) ◽  
pp. 335-346
Author(s):  
Mackenzie Simper
Keyword(s):  
Finite Group ◽  
Random Process ◽  
Uniform Distribution ◽  
Discrete Time ◽  
Random Variable ◽  
Urn Model ◽  
Infinite Type ◽  
The Mean ◽  
A Finite Group ◽  
Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

scholarly journals Sensor-based localization of epidemic sources on human mobility networks

2021 ◽  
Vol 17 (1) ◽  
pp. e1008545
Author(s):  
Jun Li ◽  
Juliane Manitz ◽  
Enrico Bertuzzo ◽  
Eric D. Kolaczyk
Keyword(s):  
Mixture Model ◽  
Human Mobility ◽  
Gaussian Mixture ◽  
Local Conditions ◽  
Arrival Times ◽  
Modes Of Transmission ◽  
Kwazulu Natal ◽  
First Arrival ◽  
Control Of Epidemics ◽  
The Impact

We investigate the source detection problem in epidemiology, which is one of the most important issues for control of epidemics. Mathematically, we reformulate the problem as one of identifying the relevant component in a multivariate Gaussian mixture model. Focusing on the study of cholera and diseases with similar modes of transmission, we calibrate the parameters of our mixture model using human mobility networks within a stochastic, spatially explicit epidemiological model for waterborne disease. Furthermore, we adopt a Bayesian perspective, so that prior information on source location can be incorporated (e.g., reflecting the impact of local conditions). Posterior-based inference is performed, which permits estimates in the form of either individual locations or regions. Importantly, our estimator only requires first-arrival times of the epidemic by putative observers, typically located only at a small proportion of nodes. The proposed method is demonstrated within the context of the 2000-2002 cholera outbreak in the KwaZulu-Natal province of South Africa.

A note on filtered Markov renewal processes

1981 ◽  
Vol 18 (03) ◽  
pp. 752-756
Author(s):  
Per Kragh Andersen
Keyword(s):  
Renewal Process ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Renewal Theorem ◽  
Markov Renewal Processes ◽  
The Moment

A Markov renewal theorem necessary for the derivation of the moment formulas for a filtered Markov renewal process stated by Marcus (1974) is proved and its applications are outlined.

License Renewal: Status of Long Term Operation in the U.S.

2008 ◽  
Author(s):  
Garry G. Young
Keyword(s):  
Public Opinion ◽  
Continuous Improvement ◽  
Renewal Process ◽  
Low Cost ◽  
Nuclear Plant ◽  
Plant Operation ◽  
Term Operation ◽  
License Renewal ◽  
The U.S

As of February 2008, the NRC has approved renewal of the operating licenses for 48 nuclear units and has applications under review for 15 more units. In addition, nuclear plant owners for at least 25 more units have announced plans to submit license renewal applications over the next few years. This brings the total of renewed licenses and announced plans for license renewal to over 80% of the 104 currently operating nuclear units in the U.S. This paper presents some of the factors that have made the U.S. license renewal process so successful. These factors include (1) the successful regulatory process and on-going continuous improvement of that process, (2) long-term safe plant operation trends, (3) stable low-cost generation of electricity, (4) high levels of plant reliability, and (5) improving public opinion trends.

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