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Dual representations of Laplace transforms of Brownian excursion and generalized meanders. (English) Zbl 1391.60180
Summary: The Laplace transform of the \(d\)-dimensional distribution of Brownian excursion is expressed as the Laplace transform of the \((d + 1)\)-dimensional distribution of an auxiliary Markov process, started from a \(\sigma\)-finite measure and with the roles of arguments and times interchanged. A similar identity holds for the Laplace transform of a generalized Brownian meander, which is expressed as the Laplace transform of the same auxiliary Markov process, with a different initial law.

MSC:
60J25 Continuous-time Markov processes on general state spaces
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