Constructing Strong Markov Processes
نویسنده
چکیده
The construction presented in this paper can be briefly described as follows: starting from any “finite-dimensional” Markov transition function pt, on a measurable state space (E,B), we construct a strong Markov process on a certain “intrinsic” state space that is, in fact, a closed subset of a finite dimensional Euclidean space R. Of course we must explain the meaning of finite-dimensionality and intrinsity. Starting with pt, we consider the range of the nonnegative bounded measurable functions under the action of the resolvent. This class of functions induces a uniform structure on E. We say that E is finite-dimensional if this uniformity is finitely generated. In such cases we then map E into R. The intrinsic state space is the closure of the range of this mapping. On this enlarged state space we construct a strong Markov process, which corresponds quite naturally to pt. We give several examples including the usual examples of nonstrong Markov process.
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