2015/03/09 by Aivar Sootla, Sootla, Aivar
Biochemistry, Genetics and Molecular Biology · Mathematics · #Evolution and Genetic Dynamics #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1503.02557
openalex publication_date 2015/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a link between monotonicity of deterministic dynamical systems and propagation of order by Markov processes is established. The order propagation has received considerable attention in the literature, however, this notion is still not fully understood. The main contribution of this paper is a study of the order propagation in the deterministic setting, which potentially can provide new techniques for analysis in the stochastic one. We take a close look at the propagation of the so-called increasing and increasing convex orders. Infinitesimal characterisations of these orders are derived, which resemble the well-known Kamke conditions for monotonicity. It is shown that increasing order is equivalent to the standard monotonicity, while the class of systems propagating the increasing convex order is equivalent to the class of monotone systems with convex vector fields. The paper is concluded by deriving a novel result on order propagating diffusion processes and an application of this result to biological processes.