Large deviation probabilities for random walks with semiexponential distributions

Alexandre A. Borovkov

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2000

ISSN 1403-9338

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Abstract:

Random walks with increment distribution F satisfying the tail assumption 1-F(t)=exp(-t^aL(t)) where 0<a<1 and L is slowly varying are considered. Large deviations result are given for the partial sums as well as for the maximum up to time n. The results include higher order expansions.