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.

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

1968 ◽  
Vol 5 (3) ◽  
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.

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.

On Stochastic Characterization of Temporal Storm Patterns

1984 ◽  
Vol 16 (8-9) ◽  
pp. 147-153 ◽  
Author(s):  
Van-Thanh-Van Nguyen
Keyword(s):  
Markov Chain ◽  
Probability Distributions ◽  
First Order ◽  
Stochastic Characterization ◽  
Order Markov Chain ◽  
Hourly Rainfall ◽  
General Stochastic Model ◽  
Storm Rainfall ◽  
Rainfall Occurrences

The present study, a continuation of a previous work by the author, suggests a new theoretical approach to the characterization of the temporal pattern of storms. A storm is defined as a continuous run of non-zero one-hour rainfall depths. A general stochastic model is developed to determine the probability distributions of cumulative storm rainfall amounts at successive time intervals after the storm began. The previous model for characterizing storm temporal patterns was based on the assumption that hourly rainfall depths were independent and identically exponentially distributed random variables, while sequences of wet hours were modeled by a first-order stationary Markov chain. Hence, the model did only introduce dependence of wet hour occurences into the rainfall process through the first-order Markov chain. The present paper proposes a more general model that can take into account both the persistence in hourly rainfall occurrences and the dependence between successive hourly rainfall depths. Results of an illustrative example show that by accounting for the correlation structure of consecutive rainfall depths the present model gives a better fit to the observations than the previous one.

On the First-Order Markov Model for the PLC Fading Channel

2013 ◽  
Vol 756-759 ◽  
pp. 2644-2648
Author(s):  
Wei Shen
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Fading Channel ◽  
Markov Models ◽  
Time Varying ◽  
Power Line Communications ◽  
Channel Response ◽  
First Order ◽  
Order Markov Chain ◽  
Time Varying Channels

The power line communications (PLC) channel is noisy one, which can be modeled by the Markov process. The order is the key concerning when used the Markov process. the level of complexity will be incurred from using higher order , while the first-order Markov models may lead to the less accurate channel response. In the paper, the first-order Markov channel is under thoroughly discussion, and it can provide a mathematically tractable model for time-varying channels and uses only the received SNR of the symbol immediately preceding the current one. With the first-order Markov chain, given the information of the symbol immediately preceding the current one, any other previous symbol should be independent of the current one. We show that given the information corresponding to the previous symbol, the amount of uncertainty remaining in the current symbol should be negligible. That means the first-order of Markov process is enough when modeled the PLC channel.

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