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  • 1995-1999  (3)
  • 60J30  (2)
  • Key words. Coarse-grained multicomputer, Parallel algorithm, Selection problem.  (1)
  • 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
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    A Note on Parallel Selection on Coarse-Grained Multicomputers (1999)
    Springer
    Algorithmica 24 (1999), S. 371-380 
    Details
    ISSN: 1432-0541
    Keywords: Key words. Coarse-grained multicomputer, Parallel algorithm, Selection problem.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Consider the selection problem of determining the k th smallest element of a set of n elements. Under the CGM (coarse-grained multicomputer) model with p processors and O(n/p) local memory, we present a deterministic parallel algorithm for the selection problem that requires O( log p) communication rounds. Besides requiring a low number of communication rounds, the algorithm also attempts to minimize the total amount of data transmitted in each round (only O(p) except in the last round). In addition to showing theoretical complexities, we present very promising experimental results obtained on a parallel machine that show almost linear speedup, indicating the efficiency and scalability of the proposed algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00008268
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    Paper (German National Licenses)
    Fulltext
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