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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
    Dominating points and large deviations for random vectors (1996)
    Springer
    Probability theory and related fields 105 (1996), S. 529-543 
    Details
    ISSN: 1432-2064
    Keywords: 60B12 ; 60F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We establish a representation formula useful for obtaining precise large deviation probabilities for convex open subsets of a Banach space. These estimates are based on the existence of dominating points in this setting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191912
    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
    Dominating points and large deviations for random vectors (1996)
    Springer
    Probability theory and related fields 105 (1996), S. 529-543 
    Details
    ISSN: 1432-2064
    Keywords: Mathematics Subject Classification (1991): 60B12 ; 60F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We establish a representation formula useful for obtaining precise large deviation probabilities for convex open subsets of a Banach space. These estimates are based on the existence of dominating points in this setting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191912
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    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)
    Fulltext
  • 6
    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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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