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On the distribution density of the supremum of a random walk in the subexponential case

✍ 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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πŸ“œ SIMILAR VOLUMES


Submultiplicative moments of the supremu
✍ M.S. Sgibnev πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 366 KB

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,

On the exact asymptotic behaviour of the
✍ M.S. Sgibnev πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 100 KB

We consider a random walk drifting to -∞ with distribution F of the steps. The paper considers the exact asymptotic behaviour of the distribution D of the supremum when there exists ¿ 0 such that R e x F(d x) = 1; R |x|e x F(d x) ‘ ∞ and R x 2 e x F(d x) = ∞, thus ÿlling the remaining gap in describ