Some zero-one laws for additive functionals of Markov processes |
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Authors: | Rainer Höhnle Karl-Theodor Sturm |
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Institution: | (1) Mathematisch-Geographische Fakultät, Universität Eichstätt, D-85071 Eichstätt, Germany;(2) Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054 Erlangen, Germany |
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Abstract: | Summary Let (X
t,P
x
) be anm-symmetric Markov process with a strictly positive transition density. Consider the additive functionalA
t
: =
0
t
f (X
s
) wheref:E 0, ] is a universally measurable function on the state spaceE. Among others, we prove thatP
x
(A
t
< )=1, for somex E and somet>0, already impliesP
x
(A
t
< )=1, for quasi everyx E and allt>0. The latter is also equivalent toP
x
(A
t
< )>0, for quasi everyx E and allt>0, and to the analytic condition
, for a sequence of finely open Borel setsF
n
such thatE F
n
is polar. In the special cases of Brownian motion and Bessel process, these results were obtained earlier by H.J. Engelbert, W. Schmidt, X.-X. Xue and the authors. |
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Keywords: | 60 J 55 60 J 57 60 J 40 |
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