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  • 1
    Electronic Resource
    Electronic Resource
    Some remarks on a question of Strassen (1996)
    Springer
    Probability theory and related fields 104 (1996), S. 211-229 
    Details
    ISSN: 1432-2064
    Keywords: Mathematics Subject classification: 60B12 ; 60F15 ; 60F17 ; 60G15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary.  Strassen’s original functional law of the iterated logarithm for partial sums and Brownian motion examined convergence and clustering in the sup-norm. Here we address what happens if we use the much larger H-norm. We provide the answer to a query which appeared at the end of Strassen’s original paper, and also present several contrasting results which are shown to be essentially best possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01247838
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The Gaussian measure of shifted balls (1994)
    Springer
    Probability theory and related fields 98 (1994), S. 143-162 
    Details
    ISSN: 1432-2064
    Keywords: 60B05 ; 60B12 ; 60G15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Let μ be a centered Gaussian measure on a Hilbert spaceH and let $$B_R \subseteq H$$ be the centered ball of radiusR〉0. Fora∈H and $$\mathop {\lim }\limits_{t{\mathbf{ }} \to {\mathbf{ }}\infty } {\mathbf{ }}R(t)/t〈 {\mathbf{ }}||a||$$ , we give the exact asymptotics of μ(B R(t)+t·a) ast→∞. Also, upper and lower bounds are given when μ is defined on an arbitrary separable Banach space. Our results range from small deviation estimates to large deviation estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01192511
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Some remarks on a question of Strassen (1996)
    Springer
    Probability theory and related fields 104 (1996), S. 211-229 
    Details
    ISSN: 1432-2064
    Keywords: 60B12 ; 60F15 ; 60F17 ; 60G15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Strassen's original functional law of the iterated logarithm for partial sums and Brownian motion examined convergence and clustering in the sup-norm. Here we address what happens if we use the much larger H-norm. We provide the answer to a query which appeared at the end of Strassen's original paper, and also present several contrasting results which are shown to be essentially best possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01247838
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    The asymptotic distribution of magnitude-Winsorized sums via self-normalization (1990)
    Springer
    Journal of theoretical probability 3 (1990), S. 137-168 
    Details
    ISSN: 1572-9230
    Keywords: Winsorized sums ; self-normalization ; trimmed sums ; magnitude order statistics ; asymptotic normality ; variance-mixtures of normals ; stochastic compactness ; weak convergence ; universal law
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Asymptotic normality, tightness, and weak convergence of the magnitude-Winsorized sums formed from symmetric i.i.d. random variables are studied via a new approach that first derives self-normalized (“studentized”) results and then uses these to derive results for constant normalizations. An application of this method to trimmed sums is also discussed to demonstrate its more general applicability as well as to illustrate its use.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01063331
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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