Multidimensional stochastic differential equations with distributional drift

By Franco Flandoli, Elena Issoglio, Francesco Russo. 2014

77 citations recorded by the source corpus.

This paper investigates a time-dependent multidimensional stochastic differential equation with drift being a distribution in a suitable class of Sobolev spaces with negative derivation order. This is done through a careful analysis of the corresponding Kolmogorov equation whose coefficient is a distribution.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/8f5ecc5290844804fe9a03573c849b82cfbdd825

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In Applied Mathematics

In Control and Systems Engineering

In Finance

Citations in the corpus

Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness (2014, background): “There are some results on weak well-posedness for measure-valued drifts, see [9], and distribution-valued drifts, see [44, 28, 15], but it is unclear whether they apply to the limit case p = d: for example, the result in [9], when restricted to measures with density b with respect to the Lebesgue me”
Rough paths and 1d SDE with a time dependent distributional drift: application to polymers (2014, background): “In this setting, unique solvability can be proved to hold in the weak or strong sense according to the regularity of Y , see for example the papers by Flandoli, Russo and Wolf [12, 13] on the one hand and the paper by Bass and Chen [3] on the other hand.”
Noiseless regularisation by noise (2020, background): “We have given a non classical notion of weak solution, which is well suited when dealing with a distributional b; depending on the context, this is not the only possible definition, see for instance [3] and [22] for different choices.”