Sequence of Random Variables with a given finite range and Conditional Expectation

• Main Authors: Chun-Hao Pan, 潘君豪
• Other Authors: Fon-Che Liu
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/99177277179510306564

碩士 === 淡江大學 === 數學學系碩士班 === 94 === 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}.