Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 2024

Diffusion Approximations of Markovian Solutions to Discontinuous ODEs

Résumé

In a companion paper, the authors have characterized all deterministic semigroups, and all Markov semigroups, whose trajectories are Carathéodory solutions to a given ODE ẋ = 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 ẋ = 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.

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hal-03993482 , version 1 (16-02-2023)

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Alberto Bressan, Marco Mazzola, Khai T Nguyen. Diffusion Approximations of Markovian Solutions to Discontinuous ODEs. Journal of Dynamics and Differential Equations, 2024, 36 (2), pp.1367-1404. ⟨10.1007/s10884-023-10250-w⟩. ⟨hal-03993482⟩
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