On a Brownian excursion law, I: convolution representations
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🧮 math.CA
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excursionbrowniangivenbelowbuiltcharacterizationconstructionconvolution
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This paper studies Brownian motion subject to the occurrence of a minimal length excursion below a given excursion level. The law of this process is determined. The characterization is explicit and shows by a layer construction how the law is built up over time in terms of the laws of sums of a given set of independent random variables.
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