Some Exact Results on Lindley Process with Laplace Jumps

Emanuele Lucrezia, Laura Sacerdote and Cristina Zucca ()
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Emanuele Lucrezia: Department of Mathematics “G.Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Laura Sacerdote: Department of Mathematics “G.Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Cristina Zucca: Department of Mathematics “G.Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Mathematics, 2025, vol. 13, issue 7, 1-36

Abstract: We consider a Lindley process with Laplace-distributed space increments. We obtain closed-form recursive expressions for the density function of the position of the process and for its first exit time distribution from the domain [ 0 , h ] . We illustrate the results in terms of the parameters of the process. An example of the application of the analytical results is discussed in the framework of the CUSUM method.

Keywords: Lindley process; random walk; Laplace distribution; first exit time; CUSUM (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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