On the distribution density of the supremum of a random walk in the subexponential case
β Scribed by D. A. Korshunov
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2006
- Tongue
- English
- Weight
- 134 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0037-4466
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π SIMILAR VOLUMES
Let {Sn } be the sequence of partial sums of independent identically distributed random variables with negative mean. Necessary and sumcient conditions are obtained for Efp(M~ ) to be finite, where ~(x) is a non-decreasing submultiplicative function, i.e. ~p(x + y)<~cp(x)c~(y), and MoΒ’ = sup{0, Si,
We consider a random walk drifting to -β with distribution F of the steps. The paper considers the exact asymptotic behaviour of the distribution D of the supremum when there exists ΒΏ 0 such that R e x F(d x) = 1; R |x|e x F(d x) Β‘ β and R x 2 e x F(d x) = β, thus ΓΏlling the remaining gap in describ