Given the (canonical) Markov process associated with a sufficiently general semigroup (P t), we establish a result concerning the uniform completeness of a family of L 2-spaces naturally associated with the jumps of the process. An application of this result is presented.
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For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.
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