• Journal of the Korean Data and Information Science Society
• /
• 제8권2호
• /
• pp.119-125
• /
• 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.

• 대한수학회지
• /
• 제35권3호
• /
• pp.727-740
• /
• 1998

Controlling traffic lights at a bottleneck, in [5] a time of open passage is called optimal, if it minimizes the first moment of the asymptotic distribution of the queue length. The discussion of the first moment as function of the time of open passage is based on an analysis of the behavior of a fixed point when varying control parameters and delivers theoretical and computational aspects of the traffic problem.

• Journal of the Korean Data and Information Science Society
• /
• 제15권4호
• /
• pp.879-889
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• 제7권1호
• /
• pp.69-78
• /
• 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 ${\mu}-RBMPx_{0}$.

• 대한수학회보
• /
• 제50권5호
• /
• pp.1659-1671
• /
• 2013

In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

• Journal of applied mathematics & informatics
• /
• 제19권1_2호
• /
• pp.475-484
• /
• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

• 응용통계연구
• /
• 제30권1호
• /
• pp.1-12
• /
• 2017

많은 확률과정이 Markov 특성을 만족하거나 근사적으로 만족하는 것으로 가정된다. Markov 과정에서 특히 관심을 끄는 것은 최초통과시간이다. 최초통과시간에 대한 연구는 Wald의 축차분석에서 시작하여 근사적 특성에 대한 많은 연구가 되어왔고 컴퓨터의 발달로 통계계산적 방법이 사용되면서 근사적 결과가 참값에 가까운 값을 계산할 수 있게 되었다. 이 논문은 Markov 과정의 예로서 지수가중 이동평균 관리도를 사용할 때 평균런길이를 계산하는 과정과 계산상의 주의점, 문제점 등을 연구하였다. 이 결과는 다른 모든 Markov 과정에 적용될 수 있으며 특히 Markov 연쇄로의 근사는 확률과정의 특성의 연구에 유용하고 계산적 접근을 용이하게 한다.

• International Journal of Reliability and Applications
• /
• 제12권1호
• /
• pp.1-14
• /
• 2011

This paper discusses the stochastic analysis and the statistical inference of a quadratic failure rate 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 random variables with quadratic failure rate, the reliability function of this system is obtained. Also, the distribution of the first passage time of this system is derived. Many important special cases are discussed.

• International Journal of Reliability and Applications
• /
• 제11권1호
• /
• pp.1-16
• /
• 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.

• 한국광학회지
• /
• 제5권2호
• /
• pp.245-251
• /
• 1994

고리형 공진기의 색소레이저에서 시계방향 모드와 반시계 방향 모드 사이에 나타나는 switching 현상을 펌프 매개변수 a, 폄프요동의 세기 Q 및 진동수폭 등을 변화시켜 Monte Carlo 방법으로 수치 계산하여 고찰하였다. 덧셈형 noise만 고려할 때와 이 noise에다 여기요동을 나타내는 곱셈형 색 noise를 포함시켰을 때 FPT분포에 미치는 영향을 조사하였다. 두 경우에 있어서 FTP의 분포는 짧은 시간영역에서는 0에서 상승하여 최대값에 도달하고, 긴 시간영역에서는 지수함수적으로 감소하는 경향은 같았으나 덧셈의 noise만 존재할 때에 비하여 곱셈의 색 noise가 포함될 때는 FPT가 감소하였다. 한편, 평균 FTP는 펌프매개변수 a의 증가와 더불어 증대하였으며 곱셈형 noise의 세기Q 및 진동수폭 $\GAMMA$가 증가할 때는 감소함을 알 수 있었다.