Evolving Systems of Stochastic Differential Equations

Leonardo Videla () and Rolando Rebolledo ()
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Leonardo Videla: Universidad de Valparaíso
Rolando Rebolledo: Universidad de Valparaíso

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1662-1705

Abstract: Abstract We introduce Evolving Systems of Stochastic Differential Equations. This model generalizes the well-known stochastic differential equations with Markovian switching, enabling the countably many local systems to have solutions in regime-dependent dimension. We provide two constructions, the first one based upon general results on measure-valued processes and the second one partially inspired by recent developments of the theory of concatenation of right processes. We prove the Feller property under very mild assumptions, provide some extensions to the basic model, and show applications of our general framework to a biological model.

Keywords: Feller property; Concatenation of Markov processes; Markov switching; Absolutely continuous change of measures; Biological models; 60J25; 60K37; 60J35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01098-1

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