2007/02/05 by Jan M. Swart, Swart, Jan M. · 1 citation
Economics, Econometrics and Finance · Mathematics · #60J80 #60K35 (Primary) #82C22 #92D25 (Secondary) #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60J80 #msc:60K35 #msc:82C22 #msc:92D25
paper · pdf · doi:10.48550/arxiv.math/0702095
Habilitation Thesis 174 pages 4 figures
arxiv created 2007/02/05 · openalex publication_date 2007/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or grows without bounds as time tends to infinity. If this is the case, then this phenomenon can often be used to determine the invariant measures, or fixed points, of the process originally under consideration, and to study convergence to equilibrium. This principle, which has been known since early work on multitype branching processes, is here demonstrated on three new examples with applications in the theory of interacting particle systems.