Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables

✍ Scribed by Allan Gut; Aurel Spătaru

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 257 KB
• Volume: 86
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1016/s0047-259x(03)00050-2

✦ Synopsis

-the positive d-dimensional lattice points with partial ordering p; let fX k ; kAZ d þ g be i.i.d. random variables with mean 0, and set S n ¼ P kpn X k ; nAZ d þ : We establish precise asymptotics for P n jnj r=pÀ2 PðjS n jXejnj 1=p Þ; and for P n ðlog jnjÞ d jnj PðjS n jX e ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi jnj log jnj p Þ; (0pdp1) as er0; and for P fn:jnjX3g 1 jnj log jnj PðjS n jXe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jnj log log jnj p Þ as er ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2ðd À 1ÞEX 2 p :