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 [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.