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A result on the Laplace transform associated with the sticky Brownian motion on an interval

Authors :
Song Shiyu
Source :
Stochastics and Dynamics. 21:2150031
Publication Year :
2020
Publisher :
World Scientific Pub Co Pte Lt, 2020.

Abstract

In this paper, we study the joint Laplace transform of the sticky Brownian motion on an interval, its occupation time at zero and its integrated process. The perturbation approach of Li and Zhou [The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab. 45 (2013) 1049–1067] is adopted to convert the problem into the computation of three Laplace transforms, which is essentially equivalent to solving the associated differential equations with boundary conditions. We obtain the explicit expression for the joint Laplace transform in terms of the modified Bessel function and Airy functions.

Details

ISSN :
17936799 and 02194937
Volume :
21
Database :
OpenAIRE
Journal :
Stochastics and Dynamics
Accession number :
edsair.doi...........3e52ef6d0ad443c7defc986153c955dc