The asymptotic behaviour of local times and occupation integrals of theN-parameter Wiener process in R
d |
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Authors: | Peter Imkeller Ferene Weisz |
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Institution: | (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 |
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Abstract: | Summary LetL(x, T),x R
d
,T R
+
N
, be the local time of theN-parameter Wiener processW taking values inR
d
. Even in the distribution valued casedd 2N,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
asT![rarr](/content/k5n8w7u374813831/xxlarge8594.gif) . 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 |
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Keywords: | 60G60 60J55 60G15 60H05 |
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