Summary
We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n−1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1≤p≤n, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n−p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.
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Hirsch, F., Song, S. Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes. Probab. Th. Rel. Fields 103, 25–43 (1995). https://doi.org/10.1007/BF01199030
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DOI: https://doi.org/10.1007/BF01199030