Couplings and Kantorovich contractions with explicit rates for diffusions
Couplings and Kantorovich contractions with explicit rates for diffusions
dc.contributor.advisor | Eberle, Andreas | |
dc.contributor.author | Zimmer, Raphael | |
dc.date.accessioned | 2020-04-24T00:06:34Z | |
dc.date.available | 2020-04-24T00:06:34Z | |
dc.date.issued | 15.09.2017 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/7212 | |
dc.description.abstract | We consider certain classes of diffusion and McKean-Vlasov processes and provide non-asymptotic quantifications of the longtime behavior using coupling methods. The thesis is divided into three main parts. In the first part, we consider ℝd valued diffusions of type In the second part, we show that a related strategy can also be applied for a class of infinite-dimensional and degenerate diffusion processes. Given a separable and real Hilbert space ℍ and a trace-class, symmetric and non-negative operator Ǥ : ℍ→ℍ we examine the equation In the third part, we present a novel approach of coupling two multidimensional and nondegenerate Itô processes ( Xt ) and ( Yt ) which follow dynamics with different drifts. The coupling is sticky in the sense that there is a stochastic process ( rt ), which solves a one-dimensional stochastic differential equation with a sticky boundary behavior at zero, such that almost surely | Xt - Yt | ≤ rt for all t ≥ 0. The coupling is constructed as a weak limit of Markovian couplings. We provide explicit, non-asymptotic and longtime stable bounds for the probability of the event { Xt = Yt }. | en |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | stochastic differential equations | |
dc.subject | Langevin diffusion | |
dc.subject | geometric ergodicity | |
dc.subject | subgeometric ergodicity | |
dc.subject | reflection coupling | |
dc.subject | Wasserstein distance | |
dc.subject | Kantorovich contraction | |
dc.subject | Lyapunov function | |
dc.subject | Harris' theorem | |
dc.subject | diffusion process | |
dc.subject | sticky boundary condition | |
dc.subject | stochastic stability | |
dc.subject | perturbations of Markov processes | |
dc.subject | total variation bounds | |
dc.subject | McKean-Vlasov | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Couplings and Kantorovich contractions with explicit rates for diffusions | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-47958 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 4795 | |
ulbbnediss.date.accepted | 27.06.2017 | |
ulbbnediss.institute | Mathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Institut für angewandte Mathematik | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Sturm, Karl-Theodor |
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