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Asymptotic of distribution of the supremum of sequential sums

✍ Scribed by V. I. Lotov

Publisher
SP MAIK Nauka/Interperiodica
Year
1985
Tongue
English
Weight
409 KB
Volume
38
Category
Article
ISSN
0001-4346

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πŸ“œ SIMILAR VOLUMES

Exact asymptotic behaviour of the distri
Exact asymptotic behaviour of the distribution of the supremum
✍ M.S. Sgibnev πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 139 KB

Asymptotic expansions are obtained for the distribution of the supremum of a random walk with negative drift. The in uence of the roots of the characteristic equation is taken into account. The exact tail behaviour of the remainder terms is determined.

On the exact asymptotic behaviour of the
On the exact asymptotic behaviour of the distribution of the supremum in the β€œcritical” case
✍ 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