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  • Electronic Resource  (2)
  • Gaussian processes  (1)
  • Strassen's LIL  (1)
  • 1
    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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  • 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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