Do, 02.11.2017, 16:15
Stability of overshoots of recurrent random walks
Oberseminar AG Stochastik

Referent: Dr. Vladislav Vysotskiy (University of Sussex)
Veranstalter: AG Stochastik
Raum: S2|15 Raum 401

Take a one-dimensional recurrent random walk, and consider the sizes of its overshoots over the zero level. It turns out that this sequence, which forms a Markov chain, always has a unique invariant distribution of a simple explicit form. The most natural way to find this
distribution is by the means of infinite ergodic theory. The question of convergence to this distribution (under no smoothness assumptions for the distribution of increments) is surprisingly hard. We were able to prove only the total variation convergence, which holds for random walks with lattice and spread out distributions (i.e., essentially, the ones with density). We also obtained the rate of this convergence under additional mild assumptions. If time allows, I will also discuss connections to
related topics: local times of random walks and the number of level-crossings, reflected and oscillating random walks, infinite ergodic theory, and renewal theory. This is a joint work with Alex Mijatovic (King's College London).



Fachbereich Mathematik
Technische Universität Darmstadt

Schlossgartenstraße 7
64289 Darmstadt

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