On some path-dependent sdes involving distributional drifts
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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