本文中第一個主題是考慮一個非馬可夫的有限值域之隨機變數序列，在滿足E(ξk+1｜ξk)=ξk的條件下的收斂性。在證明這樣的序列收斂之前，我們先給一個反例表示這樣的序列不一定是martingale。本文中第二個主題是在給定條件分配下，找到適合的機率分配，而且我們考慮最簡單的情況︰給定兩個可測的切割 {A1,...An}、{B1,...Bm}，且給定條件分配 P(Bj｜Ai)、P(Ai｜Bj)，iε{1,...,n}、jε{1,...,m}。

The first purpose of this thesis is to consider the convergence of a non-Markovian sequence taking values in a finite set which satisfies E(ξk+1｜ξk)=ξk for each k. Before the proof of convergence of such a sequence, we give an example to show that such a sequence taking values in a finite set is not a martingale in general.
The second purpose of this thesis is to find probability measures   which is compatible with apriori given conditional probabilities, and we consider the most simple situation where two measurable partitions {A1,...An} and {B1,...Bm} are given and conditional probabilities P(Bj｜Ai) and P(Ai｜Bj) are given, where  iε{1,...,n}, jε{1,...,m}.

Contents
Section 1  Introdution………………………………………………………………..1
Section 2  An Example……………………………………………………………....2
Section 3  Convergence of Non-Markovian Sequence with Finite Range…………..5
Section 4  Convergence of Non-Markovian Sequence with Countable Range……...8
Section 5  Probabilities Compatible with Given Conditional Probabilities…………9
Reference……………………………………………………………………………..17

List of Tables
Table 1…………………………………..…………………………………………….2
Table 2……………………………………………………………………………......11
Table 3………………………………………………………………………………..11

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2.A. F. Karr (1993), Probability; Springer-Verlag; New York.
3.J. Jacod & P. Protter (2000), Probability Essentials; Springer; Berlin.