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  • 1
    Electronic Resource
    Electronic Resource
    Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes (1995)
    Springer
    Probability theory and related fields 103 (1995), S. 25-43 
    Details
    ISSN: 1432-2064
    Keywords: 31C15 ; 60J25 ; 60J30 ; 60J45
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01199030
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Markov properties of multiparameter processes and capacities (1995)
    Springer
    Probability theory and related fields 103 (1995), S. 45-71 
    Details
    ISSN: 1432-2064
    Keywords: 31C15 ; 60J25 ; 60J30 ; 60J45
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study a class of multiparameter symmetric Markov processes. We prove that this class is stable by subordination in Bochner's sense. We show then that for these processes, a probabilistic and an analytic potential theory correspond to each other. In particular, additive functionals are associated with finite energy measures, hitting probabilities are estimated by capacities, quasicontinuity corresponds to path-continuity. In the last section, examples show that many earlier results, as well as new ones, in this domain can be obtained by our method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01199031
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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