在這篇論文裡，我們主要在研究$m$階馬可夫鏈下固定模式發生的期望等待時間，並解出每一種結束情況的機率。此外，考慮在不同計數下模式第二次發生的期望等待時間。

References
[1] J. C. Fu and Y. M. Chang. On probability generating functions for waiting time
distribution of compound patterns in a sequence of multistate trials. J. Appl.
Prob., 39, 70-80, 2002.
[2] H. Gerber and S. Li. The occurrence of sequence patterns in repeated experiments
and hitting times in a Markov chain. Stoch. Process. Appl., 11, 101-108, 1981.
[3] S. Li. A martingale approach to the study of occurrence of sequence pattern in
repeated experiments. Ann. Prob., 8, 1171-1176, 1980.
[4] H. Y. Lin. Duality of probabilities of runs and patterns. Masterthesis in national
university of Kaohsiung, 2005.
[5] V. Pozdnyakov, J. Glaz, M. Kulldorff, and J. M. Steele. A martingale approach
to scan statistics. Ann. Inst. Statist. Math., 57, 21-37, 2005.
[6] V. Pozdnyakov and M. Kulldorff. Waiting times for patterns and a method of
gambling teams. Amer, Math. Monthly, 113, 134-143, 2006.
[7] V. Pozdnyakov, M. Kulldorff, J. Glaz, and J. M. Steele. Gambling teams and
waiting times for patterns in two-state Markov chains. J. Appl. Prob., 43,
127-140, 2006.