Maxima of increments of partial sums for certain subexponential distributions
- Lanzinger, H.
- Stadtmüller, U.
Publication date
April 2000
DOI Publisher
Elsevier Science B.V. ISSN
0304-4149Abstract
AbstractWe consider partial sums Sn=X1+X2+⋯+Xn,n∈N, of i.i.d. random variables with moments E(X1)=0,E(X12)=σ2 and sup{t∈R:E(exp((t|X1|)1/psgn(X1))<∞}∈(0,∞) and show thatlimn→∞max0⩽j<nmax1⩽k⩽n−jSj+k−Sjϕ(k/(logn)2p−1)(logn)p=1a.s.with some explicit function ϕ(·). A related result for random variables with exponentially thin tails has recently been shown by Steinebach, extending a result given by Shao
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