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Shift invariance of the occupation time of the Brownian bridge process

✍ Scribed by Peter Howard; Kevin Zumbrun

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
71 KB
Volume
45
Category
Article
ISSN
0167-7152

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✦ Synopsis

In this note the distribution for the occupation time of a one-dimensional Brownian bridge process on any Lebesgue measurable set between the initial and ΓΏnal states of the bridge is shown to be invariant under translation and re ection, so long as the translation or re ection also lies between the initial and ΓΏnal states of the bridge. The proof employs only the strong Markov property and elementary symmetry properties of the Brownian bridge process.

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