| Summary: | 碩士 === 國立東華大學 === 應用數學研究所 === 84 === Abstract : For a given tree T and a transition probability p(x,
y) on a state space G, a tree-indexed Markov chain is defined
as follows: Given a particul-ar state x in G at a particular
vertex in T, independent Markov chains are pe-rformed according
to p(x,y) on each branch from such vertex. Our focus is on the
various recurrences of such walks , and to discuss the
difference between regular Markov chains and tree-indexed Markov
chains. In this thesis we intro-duce spectral radius,Hausdorff
dimension,Minkowski and packing dimensions anddetermine if such
tree random walks are recurrent on a given state space acc-
ording to the positiveness of such quantities.
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