### Abstract

Original language | English |
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Place of Publication | Amsterdam |

Publisher | Centrum voor Wiskunde en Informatica |

Number of pages | 19 |

Publication status | Published - 2008 |

### Publication series

Name | CWI Report |
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Volume | PNA-R0814 |

### Fingerprint

### Cite this

*Structural properties of reflected Lévy processes*. (CWI Report; Vol. PNA-R0814). Amsterdam: Centrum voor Wiskunde en Informatica.

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*Structural properties of reflected Lévy processes*. CWI Report, vol. PNA-R0814, Centrum voor Wiskunde en Informatica, Amsterdam.

**Structural properties of reflected Lévy processes.** / Andersen, L.N.; Mandjes, M.R.H.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Structural properties of reflected Lévy processes

AU - Andersen, L.N.

AU - Mandjes, M.R.H.

PY - 2008

Y1 - 2008

N2 - This paper considers a number of structural properties of reflected Lévy processes, where both onesided reflection (at 0) and two-sided reflection (at both 0 and K > 0) are examined. With Vt being the position of the reflected process at time t, we focus on the analysis of ¿(t) := EVt and ¿(t) := VarVt. We prove that for the one- and two-sided reflection we have ¿(t) is increasing and concave, whereas for the one-sided reflection we also show that ¿(t) is increasing. In most proofs we first establish the claim for the discrete-time counterpart (that is, a reflected random walk), and then we use a limiting argument. A key step in our proofs for the two-sided reflection is a new representation of the position of the reflected process in terms of the driving Lévy process.

AB - This paper considers a number of structural properties of reflected Lévy processes, where both onesided reflection (at 0) and two-sided reflection (at both 0 and K > 0) are examined. With Vt being the position of the reflected process at time t, we focus on the analysis of ¿(t) := EVt and ¿(t) := VarVt. We prove that for the one- and two-sided reflection we have ¿(t) is increasing and concave, whereas for the one-sided reflection we also show that ¿(t) is increasing. In most proofs we first establish the claim for the discrete-time counterpart (that is, a reflected random walk), and then we use a limiting argument. A key step in our proofs for the two-sided reflection is a new representation of the position of the reflected process in terms of the driving Lévy process.

M3 - Report

T3 - CWI Report

BT - Structural properties of reflected Lévy processes

PB - Centrum voor Wiskunde en Informatica

CY - Amsterdam

ER -