- Tytuł:
- An asymptotic expansion for the distribution of the supremum of a random walk
- Autorzy:
- Sgibnev, M. S.
- Powiązania:
- https://bibliotekanauki.pl/articles/1206084.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
random walk
supremum
submultiplicative function
characteristic equation
absolutely continuous component
oscillating random walk
stationary distribution
asymptotic expansions
Banach algebras
Laplace transform - Opis:
- Let ${S_n}$ be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of ${S_n}$ which takes into account the influence of the roots of the equation $1-∫_ℝe^{sx}F(dx)=0,F$ being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace transforms.
- Źródło:
-
Studia Mathematica; 2000, 140, 1; 41-55
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł