• Title, Summary, Keyword: first passage time

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An Efficient Brownian Motion Simulation Method for the Conductivity of a Digitized Composite Medium

  • Kim, In-Chan
    • Journal of Mechanical Science and Technology
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    • v.17 no.4
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    • pp.545-561
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    • 2003
  • We use the first-passage-time formulation by Torquato, Kim and Cule [J. Appl. Phys., Vol. 85, pp. 1560∼1571 (1999) ], which makes use of the first-passage region in association with the diffusion tracer's Brownian movement, and develop a new efficient Brownian motion simulation method to compute the effective conductivity of digitized composite media. By using the new method, one can remarkably enhance the speed of the Brownian walkers sampling the medium and thus reduce the computation time. In the new method, we specifically choose the first-passage regions such that they coincide with two, four, or eight digitizing units according to the dimensionality of the composite medium and the local configurations around the Brownian walkers. We first obtain explicit solutions for the relevant first-passage-time equations in two-and three-dimensions. We then apply the new method to solve the illustrative benchmark problem of estimating the effective conductivities of the checkerboard-shaped composite media. for both periodic and random configurations. Simulation results show that the new method can reduce the computation time about by an order of magnitude.

The First Passage Time of Stock Price under Stochastic Volatility

  • Nguyen, Andrew Loc
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.4
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    • pp.879-889
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    • 2004
  • This paper gives an approximation to the distribution function of the .rst passage time of stock price when volatility of stock price is modeled by a function of Ornstein-Uhlenbeck process. It also shows how to obtain the error of the approximation.

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First-Passage Time Distribution of Discrete Time Stochastic Process with 0-state

  • Park, Young-Sool
    • Journal of the Korean Data and Information Science Society
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    • v.8 no.2
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    • pp.119-125
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    • 1997
  • We handle the stochastic processes of independent and identically distributed random variables. But random variables are usually dependent among themselves in actual life. So in this paper, we find out a new process not satisfying Markov property. We investigate the probability mass functions and study on the probability of the first-passage time. Also we find out the average frequency of continuous successes in from 0 to n time.

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Average run length calculation of the EWMA control chart using the first passage time of the Markov process (Markov 과정의 최초통과시간을 이용한 지수가중 이동평균 관리도의 평균런길이의 계산)

  • Park, Changsoon
    • The Korean Journal of Applied Statistics
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    • v.30 no.1
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    • pp.1-12
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    • 2017
  • Many stochastic processes satisfy the Markov property exactly or at least approximately. An interested property in the Markov process is the first passage time. Since the sequential analysis by Wald, the approximation of the first passage time has been studied extensively. The Statistical computing technique due to the development of high-speed computers made it possible to calculate the values of the properties close to the true ones. This article introduces an exponentially weighted moving average (EWMA) control chart as an example of the Markov process, and studied how to calculate the average run length with problematic issues that should be cautioned for correct calculation. The results derived for approximation of the first passage time in this research can be applied to any of the Markov processes. Especially the approximation of the continuous time Markov process to the discrete time Markov chain is useful for the studies of the properties of the stochastic process and makes computational approaches easy.

A Distribution for Regulated ${\mu}-Brownian$ Motion Process with Control Barrier at $x_{0}$

  • Park, Young-Sool
    • Journal of the Korean Data and Information Science Society
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    • v.7 no.1
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    • pp.69-78
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    • 1996
  • Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

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Parameters Estimation of Generalized Linear Failure Rate Semi-Markov Reliability Models

  • El-Gohary, A.;Al-Khedhair, A.
    • International Journal of Reliability and Applications
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    • v.11 no.1
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    • pp.1-16
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    • 2010
  • In this paper we will discuss the stochastic analysis of a three state semi-Markov reliability model. Maximum likelihood procedure will be used to obtain the estimators of the parameters included in this reliability model. Based on the assumption that the lifetime and repair time of the system units are generalized linear failure rate random variables, the reliability function of this system is obtained. Also, the distribution of the first passage time of this system will be derived. Some important special cases are discussed.

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Switching and first-passage-time distributions in a two-mode ring dye laser (2모드 색소레이저 출력의 switching과 First-Passage-Time(FPT) 분포)

  • 박구동;신종태;김태수
    • Korean Journal of Optics and Photonics
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    • v.5 no.2
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    • pp.245-251
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    • 1994
  • The charateristics of switching between two modes in a ring dye laser has been analyzed by the Monte-Carlo computer simulation. The effect of including pump fluctuations in the first-passage-time (FPT) distributions was compared with the distribution with the quantum fluctuation. The results show the same tendency in both cases, such as steep increases from 0 to peak an exponential decrease in long time range. However the introduction of pumping fluctuation is turned out to shorten the mean FPT. The variation of the mean FPT is examined for the various fluctuationrelated parameters. The mean FPT is lengthened when pump parameter a is increased while it is shorted when Q. $\GAMMA$ are decreased. eased.

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Estimate of First-Passage Probability for Hazard Fluctuating Wind Velocity (재난 변동풍속의 최초파괴확률 평가)

  • Oh, Jong Seop;Heo, Seong Je
    • Journal of Korean Society of Disaster and Security
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    • v.6 no.2
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    • pp.23-30
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    • 2013
  • A dynamic analysis of random vibration processes is concerned with the first excursion probability based on first passage time during some specified lifetime or duration of the excitation. This study is concerned with the estimation of first-passage probability for hazard fluctuate wind velocity in the major cities reflecting the recent meteorological with largest data samples (yearly 2003-2012). The basic wind speeds were standardized homogeneously to the surface roughness category C, and to 10m above the ground surface. In this paper, the hazard fluctuate wind velocities are treated as a time-independent (stationary) random process and Gaussian random processes. The first excursion probability were calculated from Poisson model based on the independent event of level crossing & two-state Markov model based on the envelopes of level crossing.

Evaluation of Allowable Criteria in First-Passage Probability Method for Caisson Sliding of Vertical Breakwater (직립방파제의 케이슨 활동에 대한 최초통과확률법의 허용기준 산정)

  • Kim, Seung-Woo;Suh, Kyung-Duck
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.25 no.5
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    • pp.317-326
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    • 2013
  • Probabilistic design methods can consider uncertainties of design variables and are widely used in the design of vertical breakwaters. The probabilistic design methods include a partial safety factor method, reliabilitybased design method, and performance-based design method. Especially the performance-based design method calculates the accumulated sliding distance during the lifetime of the breakwater or during a design storm. Recently a time-dependent performance-based design method has been developed based on the first-passage probability of individual sliding distance during a design storm. However, because the allowable criteria in the first-passage probability method are not established, the stability of structures cannot be quantitatively evaluated. In this study, the allowable first-passage probabilities for two limit states are proposed by calculating the first-passage probabilities for the cross-sections designed with various water depths and characteristics of extreme wave height distributions. The allowable first-passage probabilities are proposed as 5% and 1%, respectively, for the repairable limit state (allowable individual sliding distance of 0.03 m) and ultimate limit state (allowable individual sliding distance of 0.1 m). The proposed criteria are applied to the evaluation of the effect of wave-height increase due to climate change on the stability of the breakwater.