臺灣博碩士論文加值系統

我們討論有關更新過程的稀分和Markov鏈稀分之性質，探討一些可由Markov鏈稀分得來之特殊的更新過程。

We study the properties of thinning and Markov chain thinning of renewal processes. Among others, we investigate whether some special renewal processes can be obtained through Markov chain thinning.

1.Introduction
2.Preliminaries
3.Some basic properties for thinning via a Markov chain
4.Delayed gamma-c renewal processes
5.Delayed negative binomial renewal processes
6.An example
7.Discussion

1.Chandramohan, J. and Liang, L. K. (1985). Bernoulli, multinomial and markov chain thinning of some point processes and some results about the superposition of dependent renewal processes. J. Appl. Prob. 22, 828-835.
2.Chung, K. L. (1974). A Course in Probability Theory, 2nd ed., Academic Press, New York.
3.Feller, W. (1971). An Introduction to Probability Theory and Its Application, Vol 2, 2nd ed., John Wiley & Sons, New York.
4.Grandell, J. (1991). Aspects of Risk Theory. Springer-Verlag, New York.
5.Isham, V. (1980). Dependent thinning of point processes. J. Appl. Prob. 17, 987-995.
6.Kolsrud, T. (1986). Some comments on thinned renewal processes. Scand. Actuarial. J. , 236-241.
7.Yannaros, N. (1988). Some comments on the inverse problem for thinned renewal processes. Scand. Actuarial J. , 113-116.
8.Yannaros, N. (1988a). On Cox processes and gamma renewal processes. J. Appl. Prob. 25, 423-427.
9.Yannaros, N. (1988b). The inverses of thinned renewal processes. J. Appl. Prob. 25, 822-828.
10. Yannaros, N. (1991). Randomly observed random walks. Commun. tatist.-Stochastic Models. 7(2), 219-231.
11.Yannaros, N. (1994). Weibull renewal processes. Ann. Inst. Statist. Math. 46, 41-648.