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  • 1
    Electronic Resource
    Electronic Resource
    Strong approximation of additive functionals (1992)
    Springer
    Journal of theoretical probability 5 (1992), S. 679-706 
    Details
    ISSN: 1572-9230
    Keywords: Additive functional ; random walk ; strong approximation ; local time ; Wiener process
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetX 1,X 2,...be a sequence of i.i.d. random variables and putS 0=0,S n =X 1+...+X n . A strong approximation type result is given forA N =∑ i=1 N f(S i ) whereF(x),x∈R is a real valued function. A similar result is given for ∫ 0 t g(B(s))ds. Some weak convergence type implications are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01058725
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Path properties of an infinite system of Wiener processes (1993)
    Springer
    Journal of theoretical probability 6 (1993), S. 353-383 
    Details
    ISSN: 1572-9230
    Keywords: Poisson process ; Wiener process ; extreme value ; strong theorems ; limit distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let πα be a Poisson process on ℝd of intensity λ and letW 1(t),W 2 (t),..., be a sequence of independent Wiener processes. LetW i (t)=X i +W i (t) whereX 1,X 2,..., are the points of πα. Consider the processess(t)=#{i:‖X i (t)‖⩽1}. These and related processes are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01047579
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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