Diffusion Approximations of Markovian Solutions to Discontinuous ODEs

Alberto Bressan, Marco Mazzola, Khai T. Nguyen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In a companion paper, the authors have characterized all deterministic semigroups, and all Markov semigroups, whose trajectories are Carathéodory solutions to a given ODE x˙=f(x), where f is a possibly discontinuous, regulated function. The present paper establishes two approximation results. Namely, every deterministic semigroup can be obtained as the pointwise limit of the flows generated by a sequence of ODEs x˙=fn(x) with smooth right hand sides. Moreover, every Markov semigroup can be obtained as limit of a sequence of diffusion processes with smooth drifts and with diffusion coefficients approaching zero.

Original languageEnglish (US)
Pages (from-to)1367-1404
Number of pages38
JournalJournal of Dynamics and Differential Equations
Volume36
Issue number2
DOIs
StatePublished - Jun 2024

All Science Journal Classification (ASJC) codes

  • Analysis

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