• 대한수학회지
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• 제38권1호
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• pp.25-35
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• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.157-172
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• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• 대한수학회지
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• 제36권1호
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.397-407
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• 2006

A new stochastic process is introduced for describing a mechanism of viruses. The process generalizes the $Bartoszy\'{n}ski's$ process ($Bartoszy\'{n}ski$, 1975a, 1975b, 1976) by allowing the stochastic perturbation between consecutive jumps to take into account the persistent infection (the infection without breaking infected cells). It is shown that the new process can be obtained by a weak limit of a sequence of Markov branching processes. Along with the construction of the new process, we study how the stochastic perturbation influences the risk of a symptom in an infected host. For this purpose, the quantal response model and the threshold model are investigated and compared through their induced survival functions.

• 지질공학
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• 제2권2호
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• pp.147-154
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• 1992

난수 발생 방법을 이용하여 시간과 규모의 영역에서 일련의 지진 발생에 대해 가상 수치 계산을 수행 했다. 가상 수치 계산의 이론은 지진 발생에 관련된 두 종류의 통계적 모델에 기초 하였다. 이들 모델들은 각기 독립적으로 발생하는 지진에 관련된 고정 포아송 처리와 여진에 관련된 분기 마르코프 처리등이다. 계산된 일련의 지진 발생들은 실제 발생한 지지의 목록과 유사함을 보여 주었다.