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  • 1
    Electronic Resource
    Electronic Resource
    Rates of clustering for some Gaussian self-similar processes (1991)
    Springer
    Probability theory and related fields 88 (1991), S. 47-75 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The analogue of Strassen's functional law of the iterated logarithm in known for many Gaussian processes which have suitable scaling properties, and here we establish rates at which this convergence takes place. We provide a new proof of the best upper bound for the convergence toK by suitably normalized Brownian motion, and then continue with this method to get similar bounds for the Brownian sheet and other self-similar Gaussian processes. The previous method, which produced these results for Brownian motion in ℝ1, was highly dependent on many special properties unavailable when dealing with other Gaussian processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01193582
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    Paper (German National Licenses)
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  • 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
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Small ball estimates for Brownian motion and the Brownian sheet (1993)
    Springer
    Journal of theoretical probability 6 (1993), S. 547-577 
    Details
    ISSN: 1572-9230
    Keywords: Brownian motion ; Brownian sheet ; Gaussian samples ; Hölder norm ; Chung's functional LIL
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Small ball estimates are obtained for Brownian motion and the Brownian sheet when balls are given by certain Hölder norms. As an application of these results we include a functional form of Chung's LIL in this setting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01066717
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    Paper (German National Licenses)
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  • 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
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Rates of clustering in Strassen's LIL for Brownian motion (1991)
    Springer
    Journal of theoretical probability 4 (1991), S. 285-309 
    Details
    ISSN: 1572-9230
    Keywords: Brownian motion ; rates of clustering ; Strassen's LIL
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If {W(t): 0≦t≦∞} denotes standard Brownian motion and then with probability one the random sequence $$\{ W(n( \cdot ))/(2nL_2 n)^{1/2} :n \geqslant 1\} $$ converges to and clusters throughoutK in the uniform norm. This is Strassen's LIL for Brownian motion, and here we examine the rate at which this convergence and clustering takes place, improving some results of K. Grill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01258738
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    Paper (German National Licenses)
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