On the area between a Lévy process with secondary jump inputs and its reflected version
Abstrak
We study the stochastic properties of the area under some function of the difference between (i) a spectrally positive Lévy process $W_t^x$ that jumps to a level $x>0$ whenever it hits zero, and (ii) its reflected version $W_t$. 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 $A_x$ of (a function of) the distance between $W_t^x$ and $W_t$ until $W_t^x$ hits zero. This result is extended in a number of directions, including the area between $A_x$ and $A_y$ and a Gaussian limit theorem. We conclude the paper with an inventory problem for which our results are particularly useful.
Topik & Kata Kunci
Penulis (2)
Offer Kella
Michel Mandjes
Akses Cepat
- Tahun Terbit
- 2023
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓