Noiseless regularisation by noise

• Lucio Galeati ^[1] ; Massimiliano Gubinelli ^[1]
  1. [1] Rheinische Friedrich-Wilhelms-Universität Bonn
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 2, 2022, págs. 433-502
• Idioma: inglés
• DOI: 10.4171/RMI/1280
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• Resumen

  • We analyse the effect of a generic continuous additive perturbation to the well-posedness of ordinary differential equations. Genericity here is understood in the sense of prevalence. This allows us to discuss these problems in a setting where we do not have to commit ourselves to any restrictive assumption on the statistical properties of the perturbation. The main result is that a generic continuous perturbation renders the Cauchy problem well-posed for arbitrarily irregular vector fields. Therefore we establish regularisation by noise “without probability”.