Shift invariance of the occupation time of the Brownian bridge process

Peter Howard and Kevin Zumbrun

Statistics & Probability Letters, 1999, vol. 45, issue 4, 379-382

Abstract: 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 final states of the bridge is shown to be invariant under translation and reflection, so long as the translation or reflection also lies between the initial and final states of the bridge. The proof employs only the strong Markov property and elementary symmetry properties of the Brownian bridge process.

Keywords: Occupation; time; Brownian; bridge (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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