Randomly switching evolution equations. (February 2021)

• Record Type: Journal Article
• Authors: Klimasara, Paweł; Mackey, Michael C.; Tomski, Andrzej; Tyran-Kamińska, Marta
• Is Part Of: Nonlinear analysis. Volume 39(2021)
• Publication Date: 2021-02
• Subjects: 35R60 -- 60J60 -- 60K37 -- 92C40; Stochastic Liouville equation -- Stochastic semigroup -- Piecewise deterministic Markov processes -- Bifurcations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100948
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: We present an investigation of stochastic evolution in which a family of evolution equations in L 1 are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the space of integrable functions. We derive equations for the first moment and correlations (of any order) of such processes. We also introduce the mean of the process at large time and describe its behaviour. The results are illustrated by some simple, yet generic, biological examples characterized by different one-parameter types of bifurcations.