The asymptotic behaviour of local times and occupation integrals of theN-parameter Wiener process in R d期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The asymptotic behaviour of local times and occupation integrals of theN-parameter Wiener process in R d

Authors:	Peter Imkeller Ferene Weisz

Affiliation:	(1) Mathematisches Institut der LMU München, Theresienstrasse 39, D-80333 München, Germany;(2) Department of Numerical Analysis, Eötvös L. University, Bogdánfy u. 10/b, H-1117 Budapest, Hungary

Abstract:	Summary LetL(x, T),xR^d,TR₊^N, be the local time of theN-parameter Wiener processW taking values inR^d. Even in the distribution valued casedd2N,L can be described in a series representation by means of multiple Wiener-Ito integrals. This setting proves to be a good starting point for the investigation of the asymptotic behaviour ofL(x, T) as \|x\|0 and/orT and of related occupation integrals $X_T (f) = intlimits_{[0,T]} f (W_S )$ asT. We obtain the rates of explosion in laws of the first order, i.e. normalized convergence laws forL(x, T) resp.X_T(f), and of the second order, i.e. normalized convergence laws forL(x, T)–E(L(x, T)) resp.X_T(f)–E(X_T(f)).This research was made during a stay at the LMU in München supported by DAAD

Keywords:	60G60 60J55 60G15 60H05
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