Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
Classical Analysis and ODEs
2021-07-06 v1 Probability
Abstract
In a companion paper, the authors have characterized all deterministic semigroups, and all Markov semigroups, whose trajectories are Carathe'odory solutions to a given ODE x'=f(x), with f possibly discontinuous. 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'=f_n(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.
Keywords
Cite
@article{arxiv.2107.01961,
title = {Diffusion Approximations of Markovian Solutions to Discontinuous ODEs},
author = {Alberto Bressan and Marco Mazzola and Khai T. Nguyen},
journal= {arXiv preprint arXiv:2107.01961},
year = {2021}
}
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38 pages