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  • Gaussian processes  (1)
  • asymptotic normality  (1)
  • convex hull for curves in ∝d  (1)
  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    Small ball probabilities for Gaussian processes with stationary increments under Hölder norms (1995)
    Springer
    Journal of theoretical probability 8 (1995), S. 361-386 
    Details
    ISSN: 1572-9230
    Keywords: Gaussian processes ; small ball probabilities ; the law of the iterated logarithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Small ball probabilities are estimated for Gaussian processes with stationary increments when the small balls are given by various Hölder norms. As an application we establish results related to Chung's functional law of the iterated logarithm for fractional Brownian motion under Hölder norms. In particular, we identify the points approached slowest in the functional law of the iterated logarithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02212884
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On Convex Limit Sets and Brownian Motion (1998)
    Springer
    Journal of theoretical probability 11 (1998), S. 461-492 
    Details
    ISSN: 1572-9230
    Keywords: Brownian motion ; Brownian sheet ; convex hull for curves in ∝d ; extended convex hulls ; law of the iterated logarithm in Banach spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove limsup results for nonnegative functionals of convex sets determined by normalized Brownian paths in Banach spaces. This continues the interesting investigation of D. Khoshnevisan into this area, and relates to some classical unsolved isoperimetric problems for the convex hull of curves in ∝d. Section 4 contains the solution of a problem similar to these classical problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022640007525
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    Paper (German National Licenses)
    Fulltext
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