Year: 2024
Type: article
Abstract: .We study the stochastic properties of the area under some function of the difference between (i) a spectrally positive Lévy process Wtx that jumps to a level x > 0 whenever it hits zero and (ii) its reflected version Wt. Remarkably, even though the analysis of each of these areas is challenging, we succeed in attaining explicit expressions for their difference. The main result concerns the Laplace-Stieltjes transform of the integral Ax of (a function of) the distance between Wtx and Wt until Wtx hits zero. This result is extended in a number of directions, including the area between Ax and Ay and a Gaussian limit theorem. We conclude the article with an inventory problem for which our results are particularly useful.
Source: Stochastic Models
Authors: Offer Kella, Michel Mandjes
Institutions: Hebrew University of Jerusalem, Leiden University
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Award: G565383568
OpenAlex ID: W4402276756