TY - JOUR
T1 - Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
AU - Bressan, Alberto
AU - Mazzola, Marco
AU - Nguyen, Khai T.
N1 - Funding Information:
This research by K. T. Nguyen was partially supported by a Grant from the Simons Foundation/SFARI (521811, NTK).
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85149345049&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85149345049&partnerID=8YFLogxK
U2 - 10.1007/s10884-023-10250-w
DO - 10.1007/s10884-023-10250-w
M3 - Article
AN - SCOPUS:85149345049
SN - 1040-7294
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
ER -