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Pré-Publication, Document De Travail Année : 2020

On some path-dependent sdes involving distributional drifts

Alberto Ohashi
  • Fonction : Auteur
Alan Teixeira
  • Fonction : Auteur

Résumé

This paper investigates some one-dimensional path-dependent SDEs, which includes an irregular (distributional) drift b′ depending on the present position. We treat essentially two cases: the first one concerns the case when the drift b′ is the derivative of a continuous function, the second one when b ′ is the derivative of a logarithmic or an Heaviside function. In the second framework, we characterize Bessel processes in low dimension as unique solutions to some suitable strong martingale problems and we consider then path-dependent extensions.
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Dates et versions

hal-02465590 , version 1 (04-02-2020)
hal-02465590 , version 2 (20-05-2021)

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Alberto Ohashi, Francesco Russo, Alan Teixeira. On some path-dependent sdes involving distributional drifts. 2020. ⟨hal-02465590v1⟩
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