Noiseless regularisation by noise

By Lucio Galeati, Massimiliano Gubinelli. Revista matemática iberoamericana, 2020

56 citations recorded by the source corpus.

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".

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/6c26a04b5bca061bd12fe3c3f86a5d2287608944

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Lucio Galeati
2. Avi Mayorcas
3. Fabian A. Harang

In Control and Systems Engineering

1. Lucio Galeati
2. Avi Mayorcas
3. Fabian A. Harang

In Finance

1. Lucio Galeati
2. Avi Mayorcas
3. Fabian A. Harang

Citations in the corpus

• Distribution dependent SDEs driven by additive fractional Brownian motion (2021, background): “5) see for instance Theorem 15 and Corollary 2 from [17].”