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.
Some Exact Results on Lindley Process with Laplace Jumps
Lucrezia E.;Sacerdote L.;Zucca C.
2025-01-01
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.
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