Dual representations of Laplace transforms of Brownian excursion and generalized meanders

Abstract

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 meander, which is expressed as the Laplace transform of the same auxiliary Markov process, with a different initial law.

minor revision

References in corpus (4)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
• The local structure of $q$-Gaussian processes
• Extremes of $q$-Ornstein-Uhlenbeck processes

Cited by in corpus (5)

• Markov processes related to the stationary measure for the open KPZ equation
• Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
• From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval
• Steady state of the KPZ equation on an interval and Liouville quantum mechanics
• Fluctuations of random Motzkin paths