Work

Regularity of the stationary density for systems with fast random switching

Year: 2025

Type: article

Abstract: We consider the piecewise-deterministic Markov process obtained by randomly switching between the flows generated by a finite set of smooth vector fields on a compact set. We obtain Hörmander-type conditions on the vector fields guaranteeing that the stationary density is: Ck whenever the jump rates are sufficiently fast, for any k < ∞ ; unbounded whenever the jump rates are sufficiently slow and lower semicontinuous regardless of the jump rates. Our proofs are probabilistic, relying on a novel application of stopping times.

Source: Nonlinearity

DOI: 10.1088/1361-6544/adeef8

Authors: Michel Benaïm, Oliver Tough

Institutions: University of Neuchâtel, Durham University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Engineering and Physical Sciences Research Council