A Study of Individual Number Process Under Continuous-Time Markov Chains

시간이 연속인 마르코프 체인하에서 개체수 과정에 관한 연구

In this paper, the individual number of the future has depended not only upon the present individual number but upon the present individual age, considering the stochastic process model of individual number when the life span of each individual number and the individual age as a set, this becomes a Markovian. Therefore, in this paper the individual is treated as invariable, without depending upon the whole record of each individual since its birth. As a result, suppose {N(t), t>0} be a counting process and also suppose $Z_n$ denote the life span between the (n-1)st and the nth event of this process, (n{$geq}1$) : that is, when the first individual is established at n=1(time, 0), the Z$Z_n$ at time nth individual breaks, down. Random walk $Z_n$ is $Z_n=X_1+X_2+{\cdots}{\cdots}+X_A, Z_0=0$ So, fixed time t, the stochastic model is made up as follows ; A) Recurrence (Regeneration)number between(0.t) $N_t=max{n ; Z_n{\leq}t}$ B) Forwardrecurrence time(Excess life) $T^-I_t=Z_{Nt+1}-t$ C) Backward recurrence time(Current life) $T^-_t=t-Z_{Nt}$