Multidimensional stochastic differential equations with distributional drift

  • Flandoli F
  • Issoglio E
  • Russo F
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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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Flandoli, F., Issoglio, E., & Russo, F. (2016). Multidimensional stochastic differential equations with distributional drift. Transactions of the American Mathematical Society, 369(3), 1665–1688. https://doi.org/10.1090/tran/6729

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