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...
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MDPI AG
2025-04-01
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| 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 |
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