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| Abstract |
Let $ (Omega, mathcal{F}) $ be a measurable space where $ mathcal{F} $ is generated by a sequence of functions $ mathbf{X} = {X_k} $. A probability measure $ mathbf{P} $ on $ (Omega, mathcal{F}) $ is ...Markovian iff $ mathbf{X} $ is a Markov chain on $ (Omega, mathcal{F}, mathbf{P}) $. The aim of this paper is to characterize the absolute continuity of locally equivalent Markovian measures on $ (Omega, mathcal{F}) $ in terms of transition probabilities. Especially we shall investigate the Markovian measures with transition densities and give a sufficient condition for a sequence $ mathbf{a} = {a_k} in l_2 $ to be admissible. The Markovian measures with a discrete state are also investigated and, for a finite state space, a necessary and sufficient condition for an ⅡD and a Markov chain to be equivalent shall be given.show more
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