隨機漫步在機率空間之探討

Some discussions of the random walk on probability space

王有緣(Yu-Yuan Wang)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2014年)

https://doi.org/10.6840/cycu201400165

摘要

機率是最吸引的主題之一，以分子在空間的移動情形
為例，將它轉化成一個隨機行為，並引進了機率的概念而加
以探討。本文對於Probability(Karr，1993)這本書第0 章
隨機漫步中有關第一種反射率，舉例說明他們的證明方式是
有問題的，因此我們提出遞迴及Catalan number 的方法去
取代前一種方法來證明反射率的性質。

關鍵字

隨機漫步 ； 機率

並列摘要

Probability has long been one of the subjects that
attract me most. This researcher takes the moving
molecular in the space as an example to transform it as a Random Walk, and study it through employing the concepts of the probability. This thesis manifests it can not prove its certain consequence following the theory of the first type of the reflex rate in the zero chapter of the Random Walk of the probability book by Karr,
1993 s. Hence this researcher adopts the methods
of the convolution and Catalan number to substitute the previous method to identify the nature of the reflex rate, and it has got preliminary affirmative outcome.

並列關鍵字

probability ； random walk

參考文獻

1. Alan, F. Karr. (1993). Probability (Springer Texts in Statistics). Spring-Verlag.

2. Chen Chuan-Chong and Koh Khee-Meng. (1992). Principles and Techniques in

Combinatorics. World Scientific.