2015/11/19 by José Luis Pérez, Pérez, José-Luis, Kazutoshi Yamazaki +1
Business, Management and Accounting · Decision Sciences · Mathematics · #60G51 #90B22 #91B30 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1511.06027
openalex publication_date 2015/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a combination of the refracted and reflected Lévy processes. Given a spectrally negative Lévy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a constant rate is subtracted from the increments of the process. Using the scale functions, we compute the resolvent measure, the Laplace transform of the occupation times as well as other fluctuation identities that will be useful in applied probability including insurance, queues, and inventory management.