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Multidimensional stochastic differential equations with distributional drift


Authors: Franco Flandoli, Elena Issoglio and Francesco Russo
Journal: Trans. Amer. Math. Soc. 369 (2017), 1665-1688
MSC (2010): Primary 60H10, 35K10, 60H30, 35B65
DOI: https://doi.org/10.1090/tran/6729
Published electronically: June 20, 2016
MathSciNet review: 3581216
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Abstract: 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.


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Additional Information

Franco Flandoli
Affiliation: Dipartimento Matematica, Largo Bruno Pontecorvo 5, C.A.P. 56127, Pisa, Italia
Email: flandoli@dma.unipi.it

Elena Issoglio
Affiliation: Department of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
Email: E.Issoglio@leeds.ac.uk

Francesco Russo
Affiliation: Unité de Mathématiques Appliquées, ENSTA ParisTech, Université Paris-Saclay, 828, boulevard des Maréchaux, F-91120 Palaiseau, France
Email: francesco.russo@ensta-paristech.fr

DOI: https://doi.org/10.1090/tran/6729
Keywords: Stochastic differential equations, distributional drift, Kolmogorov equation
Received by editor(s): January 23, 2014
Received by editor(s) in revised form: December 17, 2014, and March 4, 2015
Published electronically: June 20, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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