Some Exact Results on Lindley Process with Laplace Jumps

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math...

Full description

Saved in:
Bibliographic Details
Main Authors: Emanuele Lucrezia, Laura Sacerdote, Cristina Zucca
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/7/1166
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849738825380659200
author Emanuele Lucrezia
Laura Sacerdote
Cristina Zucca
author_facet Emanuele Lucrezia
Laura Sacerdote
Cristina Zucca
author_sort Emanuele Lucrezia
collection DOAJ
description 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>h</mi><mo>]</mo></mrow></semantics></math></inline-formula>. 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.
format Article
id doaj-art-74c8ac76d0114d95b5b7cc789f704a1e
institution DOAJ
issn 2227-7390
language English
publishDate 2025-04-01
publisher MDPI AG
record_format Article
series Mathematics
spelling doaj-art-74c8ac76d0114d95b5b7cc789f704a1e2025-08-20T03:06:27ZengMDPI AGMathematics2227-73902025-04-01137116610.3390/math13071166Some Exact Results on Lindley Process with Laplace JumpsEmanuele Lucrezia0Laura Sacerdote1Cristina Zucca2Department of Mathematics “G.Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, ItalyDepartment of Mathematics “G.Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, ItalyDepartment of Mathematics “G.Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, ItalyWe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>h</mi><mo>]</mo></mrow></semantics></math></inline-formula>. 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.https://www.mdpi.com/2227-7390/13/7/1166Lindley processrandom walkLaplace distributionfirst exit timeCUSUM
spellingShingle Emanuele Lucrezia
Laura Sacerdote
Cristina Zucca
Some Exact Results on Lindley Process with Laplace Jumps
Mathematics
Lindley process
random walk
Laplace distribution
first exit time
CUSUM
title Some Exact Results on Lindley Process with Laplace Jumps
title_full Some Exact Results on Lindley Process with Laplace Jumps
title_fullStr Some Exact Results on Lindley Process with Laplace Jumps
title_full_unstemmed Some Exact Results on Lindley Process with Laplace Jumps
title_short Some Exact Results on Lindley Process with Laplace Jumps
title_sort some exact results on lindley process with laplace jumps
topic Lindley process
random walk
Laplace distribution
first exit time
CUSUM
url https://www.mdpi.com/2227-7390/13/7/1166
work_keys_str_mv AT emanuelelucrezia someexactresultsonlindleyprocesswithlaplacejumps
AT laurasacerdote someexactresultsonlindleyprocesswithlaplacejumps
AT cristinazucca someexactresultsonlindleyprocesswithlaplacejumps