Mo. 18.11.24, Mathematisches Kolloquium

Thema: On Friendships of Lévy and Markov additive processes. Referent: Prof. Dr. Lukas Trottner (Universität Birmingham), Zeit: 14:30 Uhr, Raum: ENC-D 120

Mathematisches Kolloquium 

 

On Friendships of Lévy and Markov additive processes

 

Montag, den 18.11.24, um 14:30 Uhr,  Raum ENC-D 120

 

Referent:

  Prof. Dr. Lukas Trottner

 

(Universität Birmingham)

 

Abstrakt: The Wiener–Hopf factorisation of a Lévy process describes how the sample path achieves new maxima and minima in terms of a pair of subordinators. Vigon’s theory of friendship and philanthropy deals with the inverse problem of finding necessary and sufficient criteria for two given subordinators to form a valid Wiener–Hopf factorisation. In this talk, we deal with the analogous problem for Markov additive processes (MAPs). We prove a “Theorem of friends” and use our results to construct MAPs with explicit Wiener–Hopf factorisations. Such friendships are given probabilistic meaning if the Wiener–Hopf factorisation is unique. We prove the general uniqueness result for Lévy processes and discuss some partial results for MAP factorisations. This talk is based on joint works with Leif Döring, Mladen Savov and Alex Watson.

 

 

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