A Lyapunov approach to stability of positive semigroups: an overview with illustrations

• Published in: Stochastic analysis and applications Vol. 42; no. 1; pp. 121 - 200
• Main Authors: Arnaudon, Marc, Del Moral, Pierre, Ouhabaz, El Maati
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.01.2024; Taylor & Francis Ltd; Taylor & Francis: STM, Behavioural Science and Public Health Titles
• Subjects: Applications of mathematics; Boundary conditions; boundary problems; Branching (mathematics); Dirichlet problem; Harmonic oscillators; Hyperspaces; hypersurfaces; Integral operators; Langevin diffusions; Liapunov functions; Lyapunov function; Markov and Sub-Markov semigroups; Markov processes; Mathematics; Molecular composites; Neumann problem; Primary 47D08; Probability; secondary 47B65; Semigroups; shape matrices; Stability analysis; Stochastic processes; Integral operators; Markov and Sub-Markov semigroups; hypersurfaces; harmonic oscillators; Langevin diffusions; semigroups; shape matrices; Lyapunov function

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 filteri...