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  • 1
    Electronic Resource
    Electronic Resource
    Rates of convergence for increments of Brownian motion (1988)
    Springer
    Journal of theoretical probability 1 (1988), S. 27-63 
    Details
    ISSN: 1572-9230
    Keywords: Brownian motion ; Gaussian measures ; Strassen's law of the iterated logarithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The results of this paper concern rates of convergence for increments of Brownian motion. As a by-product we give some improvements of a result of Bolthausen dealing with Strassen's law of the iterated logarithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01076287
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    Paper (German National Licenses)
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  • 2
    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)
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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
    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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