Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force

We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted $L^{\infty}$ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force

Procedures for model-guided data analysis of chromosomal loci dynamics at short time scales

International audienc

Host race formation in the Acari

Host race formation generates diversity within species and may even lead to speciation. This phenomenon could be particularly prevalent in the Acari due to the often intimate interaction these species have with their hosts. In this review, we explore the process of host race formation, whether it is likely to occur in this group and what features may favour its evolution. Although few studies are currently available and tend to be biased toward two model species, results suggest that host races are indeed common in this group, and more likely to occur when hosts are long-lived. We discuss future directions for research on host-associated adaptations in this group of organisms and the potential relevance of host race formation for the biodiversity of mites and ticks