Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
| Autor: | Alberto Bressan, Marco Mazzola, Khai T. Nguyen |
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| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2107.01961 |
| Popis: | 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. Comment: 38 pages |
| Databáze: | OpenAIRE |
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