First-emptiness problems in applied probability under first-order dependent input and general output conditions

1973 ◽  
Vol 10 (02) ◽  
pp. 330-342 ◽  
Author(s):  
J. P. Lehoczky
Keyword(s):  
Markov Chain ◽  
Integral Functional ◽  
Applied Probability ◽  
Input Process ◽  
First Order ◽  
Infinite Reservoir

Results for the first-emptiness time of a semi-infinite reservoir and the integral functional of the process up to first-emptiness time are derived under Markov chain input conditions and general output conditions. The results are further extended to allow an input process which is the sum of k consecutive elements of the Markov chain, k ≧ 1.

First-emptiness problems in applied probability under first-order dependent input and general output conditions

1973 ◽  
Vol 10 (2) ◽  
pp. 330-342 ◽  
Author(s):  
J. P. Lehoczky
Keyword(s):  
Markov Chain ◽  
Integral Functional ◽  
Applied Probability ◽  
Input Process ◽  
First Order ◽  
Infinite Reservoir

Results for the first-emptiness time of a semi-infinite reservoir and the integral functional of the process up to first-emptiness time are derived under Markov chain input conditions and general output conditions. The results are further extended to allow an input process which is the sum of k consecutive elements of the Markov chain, k ≧ 1.

Nappes d'huile: prediction de leurs deplacements comme agent efficace d'un plan de mesure d'urgence

1979 ◽  
Vol 14 (1) ◽  
pp. 89-109
Author(s):  
B. Coupal ◽  
M. de Broissia
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Finite Elements ◽  
Mass Balance ◽  
Stochastic Method ◽  
Stochastic Methods ◽  
Deterministic Approach ◽  
First Order ◽  
The Third ◽  
Comme Agent

Abstract The movement of oil slicks on open waters has been predicted, using both deterministic and stochastic methods. The first method, named slick rose, consists in locating an area specifying the position of the slick during the first hours after the spill. The second method combines a deterministic approach for the simulation of current parameters to a stochastic method simulating the wind parameters. A Markov chain of the first order followed by a Monte Carlo approach enables the simulation of both phenomena. The third method presented in this paper describes a mass balance on the spilt oil, solved by the method of finite elements. The three methods are complementary to each other and constitute an important point for a contingency plan.

Online to offline social interaction on gaming motivations

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wei-Lun Chang ◽  
Li-Ming Chen ◽  
Yen-Hao Hsieh
Keyword(s):  
Markov Chain ◽  
Online Games ◽  
Online Gaming ◽  
Online Game ◽  
Content Type ◽  
Switching Model ◽  
First Order ◽  
Order Markov Chain ◽  
Game Players ◽  
Motivation Model

PurposeThis research examined the social interactions of online game players based on the proposed motivation model in order to understand the transitions of motivation of online game. The authors also separated samples into four categories to compare the difference of different type of online game players.Design/methodology/approachThis study proposed a motivation model for online game player based on existence–relatedness–growth theory. The authors also analyze the transitions of motivations via first-order and second-order Markov chain switching model to obtain the journey of online to offline socialization.FindingsTeamwork–socialization players preferred to make friends in their online gaming network to socialize. Competition–socialization players were mostly students who played games to compete and socialize and may share experience in online or offline activities. Teamwork–mechanics players purely derived pleasure from gaming and were not motivated by other factors in their gaming activities. Competition–mechanics players may already have friends with other gamers in real life.Research limitations/implicationsMore samples can be added to generate more generalizable findings and the proposed motivation model can be extended by other motivations related to online gaming behavior. The authors proposed a motivation model for online to offline socialization and separated online game players into four categories: teamwork–socialization, competition–socialization, teamwork–mechanics and competition–mechanics. The category of teamwork–socialization may contribute to online to offline socialization area. The category of competition–mechanics may add value to the area of traditional offline socialization. The categories of competition–socialization and teamwork–mechanics may help extant literature understand critical stimulus for online gaming behavior.Practical implicationsThe authors’ findings can help online gaming industry understand the motivation journey of players through transition. Different types of online games may have various online game player's journey that can assist companies in improving the quality of online games. Online game companies can also offer official community to players for further interaction and experience exchange or the platform for offline activities in the physical environment.Originality/valueThis research proposed a novel motivation model to examine online to offline socializing behavior for online game research. The motivations in model were interconnected via the support of literature. The authors also integrated motivations by Markov chain switching model to obtain the transitions of motivational status. It is also the first attempt to analyze first-order and second-order Markov chain switching model for analysis. The authors’ research examined the interconnected relationships among motivations in addition to the influential factors to online gaming behavior from previous research. The results may contribute to extend the understanding of online to offline socialization in online gaming literature.

International Real Estate Review

2016 ◽  
Vol 19 (3) ◽  
pp. 265-296
Author(s):  
Richard D. Evans ◽  
◽  
Glenn R. Mueller ◽  
Keyword(s):  
Markov Chain ◽  
Real Estate ◽  
Cash Flow ◽  
Discounted Cash Flow ◽  
First Order ◽  
Order Markov Chain ◽  
Office Markets ◽  
Speed Up ◽  
Staying Time ◽  
Over Time

Metro market real estate cycles for office, industrial, retail, apartment, and hotel properties may be specified as first order Markov chains, which allow analysts to use a well-developed application, ¡§staying time¡¨. Anticipations for time spent at each cycle point are consistent with the perception of analysts that these cycle changes speed up, slow down, and pause over time. We find that these five different property types in U.S. markets appear to have different first order Markov chain specifications, with different staying time characteristics. Each of the five property types have their longest mean staying time at the troughs of recessions. Moreover, industrial and office markets have much longer mean staying times in very poor trough conditions. Most of the shortest mean staying times are in hyper supply and recession phases, with the range across property types being narrow in these cycle points. Analysts and investors should be able to use this research to better estimate future occupancy and rent estimates in their discounted cash flow (DCF) models.

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Determination of the Order of a Markov Chain for Daily Rainfall Data of North East India: "Application AIC criterion"

2018 ◽  
Vol 10 (1) ◽  
pp. 80-87
Author(s):  
Surobhi Deka
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Akaike Information Criterion ◽  
Markov Chain Model ◽  
Information Criterion ◽  
Chain Model ◽  
Adequate Model ◽  
First Order ◽  
North East India ◽  
North East

The paper aims at demonstrating the application of the Akaike information criterion to determine the order of two state Markov chain for studying the pattern of occurrence of wet and dry days during the rainy season (April to September) in North-East India. For each station, each day is classified as dry day if the amount of rainfall is less than 3 mm and wet day if the amount of rainfall is greater than or equal to 3 mm. We apply Markov chain of order up to three to the sequences of wet and dry days observed at seven distantly located stations in North East region of India. The Markov chain model of appropriate order for analyzing wet and dry days is determined. This is done using the Akaike Information Criterion (AIC) by checking the minimum of AIC estimate. Markov chain of order one is found to be superior to the majority of the stations in comparison to the other order Markov chains. More precisely, first order Markov chain model is an adequate model for the stations North Bank, Tocklai, Silcoorie, Mohanbari and Guwahati. Further, it is observed that second order and third order Markov chains are competing with first order in the stations Cherrapunji and Imphal, respectively. A fore-knowledge of rainfall pattern is of immense help not only to farmers, but also to the authorities concerned with planning of irrigation schemes. The outcomes are useful for taking decisions well in advance for transplanting of rice as well as for other input management and farm activities during different stages of the crop growing season.

Semi-Markov Replacement Chains

1994 ◽  
Vol 26 (3) ◽  
pp. 728-755 ◽  
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
Markov Chain ◽  
Control Theory ◽  
Markov Chains ◽  
Time Dependent ◽  
Applied Probability ◽  
Probability Models ◽  
Natural Manner ◽  
Environmental Behaviour ◽  
New Process

We consider an absorbing semi-Markov chain for which each time absorption occurs there is a resetting of the chain according to some initial (replacement) distribution. The new process is a semi-Markov replacement chain and we study its properties in terms of those of the imbedded Markov replacement chain. A time-dependent version of the model is also defined and analysed asymptotically for two types of environmental behaviour, i.e. either convergent or cyclic. The results contribute to the control theory of semi-Markov chains and extend in a natural manner a wide variety of applied probability models. An application to the modelling of populations with semi-Markovian replacements is also presented.

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