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  • 1
    Electronic Resource
    Electronic Resource
    Two principles for extending probability measures (1977)
    Springer
    Manuscripta mathematica 21 (1977), S. 43-50 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A principle for proving the existence of an extension of a probability measure and a principle which answers the question of uniqueness of the extension are given. It turns out that these principles can be applied in a great number of situations treated in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01176900
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  • 2
    Electronic Resource
    Electronic Resource
    On the structure of quadratic congruential sequences (1987)
    Springer
    Manuscripta mathematica 58 (1987), S. 129-140 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sequences of integers defined by a quadratic congruential formula are divided into non-overlapping subsequences of length d. The structure of the set of the resulting points in the d-dimensional Euclidean space Rd is studied. The analysis is restricted to the case of sequences with maximal period length since such sequences are of special interest in connection with pseudo random number generation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01169087
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  • 3
    Electronic Resource
    Electronic Resource
    A multiple recursive non-linear congruential pseudo random number generator (1987)
    Springer
    Manuscripta mathematica 59 (1987), S. 331-346 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract On-linear multiple recursive congruential pseudo random number generator with prime modulus p is introduced. Let x, n≥0, be the sequence generated by a usual linear (r+1)-step recursive congruential generator with prime modulus p and denote by N(n), n≥0, the sequence of non-negative integers with xN(n)≢0 (mod p). The non-linear generator is defined by zn≡xN(n)+1·x N(n) −1 (mod p), n≥0, where x N(n) −1 denotes the inverse element of xN(n) in the Galois field GF(p). A condition is given which ensures that the generated sequence is purely periodic with period length pr and all (p−1)r r-tupels (y1,...,yr) with 1≤y1,...,yr≤p are generated once per period when r-tupels of consecutive numbers of the generated sequence are formed. For r=1 this generator coincides with the generator introduced by Eichenauer and Lehn [2].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01174798
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  • 4
    Electronic Resource
    Electronic Resource
    Prämessbare Funktionen (1977)
    Springer
    Manuscripta mathematica 20 (1977), S. 141-152 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (X,A,p) be a complete probability space. A function f: X→ℝ is called premeasurable, if there is a measure extension of p defined on the б-algebra generated byA and the function f. Several classes of premeasurable functions are studied here. This paper is a continuation of Bierlein's investigations in [2], [3] and [4]. The basic ideas and notations can be found there.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170722
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  • 5
    Electronic Resource
    Electronic Resource
    Ma\fortsetzungen und Aumann's Selektionstheorem (1976)
    Springer
    Probability theory and related fields 35 (1976), S. 265-268 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00532678
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  • 6
    Electronic Resource
    Electronic Resource
    On the uniqueness of pre-image measures (1977)
    Springer
    Probability theory and related fields 38 (1977), S. 333-337 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A necessary and sufficient condition for the uniqueness of the pre-image measure in the situation studied by Yershov [8] and other authors [4, 5] is given. This very natural condition, different from that in [8], has been discovered by Eisele [2] under more restrictive assumptions. Our main theorem extends this result to the situation considered by Yershov.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00533165
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  • 7
    Electronic Resource
    Electronic Resource
    Gamma-minimax estimators for the mean of a multivariate normal distribution with partially unknown covariance matrix (1995)
    Springer
    Acta mathematicae applicatae sinica 11 (1995), S. 11-16 
    Details
    ISSN: 1618-3932
    Keywords: Bayes estimation ; minimax estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper Γ-minimax estimation of a multivariate normal mean under arbitrary squared error loss is considered where the covariance matrix of the normal distribution is a known symmetric and positive definite matrix with unknown multiple. The set Γ is fixed by imposing restrictions on the vector of first moments and on the matrix of second moments as well as on the first moment of the unknown factor determining of the covariance matrix. Necessary and sufficient conditions are derived which ensure that an estimator is Γ-minimax and that a prior is least favorable in Γ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02012618
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