✦ LIBER ✦

On asymptotic independence of the exit moment and position from a small domain for diffusion processes

✍ Scribed by Vitalii A. Gasanenko

Book ID: 111487624
Publisher: SP Versita
Year: 2003
Tongue: English
Weight: 214 KB
Volume: 1
Category: Article
ISSN: 1895-1074
DOI: 10.2478/bf02475666

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

If ξ(t) is the solution of homogeneous SDE in R
m, and T
∃ is the first exit moment of the process from a small domain D
∃, then the total expansion for the following functional showing independence of the exit time and exit place is
$$Eexp( - \lambda T_\varepsilon )f(\frac{{\xi (T_\varepsilon )}}{\varepsilon }) - Eexp( - \lambda T_\varepsilon )Ef(\frac{{\xi (T_\varepsilon )}}{\varepsilon }),\varepsilon \searrow 0,\lambda > 0.$$

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