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A Lyapunov approach to stability of positive semigroups: An overview with illustrations
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ARNAUDON, Marc | |
| hal.structure.identifier | Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL] | |
| dc.contributor.author | MORAL, Pierre | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAATI OUHABAZ, El | |
| dc.date.accessioned | 2024-04-04T02:36:33Z | |
| dc.date.available | 2024-04-04T02:36:33Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190729 | |
| dc.description.abstractEn | The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety of areas of applied mathematics, including nonlinear filtering, rare event analysis, branching processes, physics and molecular chemistry. This article presents an overview of some recent Lyapunov-based approaches, focusing principally on practical and powerful tools for designing Lyapunov functions. These techniques include semigroup comparisons as well as conjugacy principles on non necessarily bounded manifolds with locally Lipschitz boundaries. All the Lyapunov methodologies discussed in the article are illustrated in a variety of situations, ranging from conventional Markov semigroups on general state spaces to more sophisticated conditional stochastic processes possibly restricted to some non necessarily bounded domains, including locally Lipschitz and smooth hypersurface boundaries, Langevin diffusions as well as coupled harmonic oscillators. | |
| dc.language.iso | en | |
| dc.subject.en | Integral operators | |
| dc.subject.en | semigroups | |
| dc.subject.en | Markov and Sub-Markov semigroups | |
| dc.subject.en | harmonic oscillators | |
| dc.subject.en | Langevin diffusions | |
| dc.subject.en | Lyapunov function | |
| dc.subject.en | hypersurfaces | |
| dc.subject.en | shape matrices | |
| dc.title.en | A Lyapunov approach to stability of positive semigroups: An overview with illustrations | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 2301.03484 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03931007 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03931007v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ARNAUDON,%20Marc&MORAL,%20Pierre&MAATI%20OUHABAZ,%20El&rft.genre=preprint |
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