where the drift
is either a measure or an integrable function, and
is a
-dimensional
fractional Brownian motion with Hurst parameter
,
. For the
case where
,
,
we show weak existence of solutions to this equation under the condition
which is an extension of the Krylov–Röckner condition (2005) to the fractional
case. We construct a counterexample showing optimality of this condition. If
is a Radon measure, particularly the delta measure, we prove
weak existence of solutions to this equation under the optimal
condition .
We also show strong well-posedness of solutions to this equation under certain
conditions. To establish these results, we utilize the stochastic sewing technique and
develop a new version of the stochastic sewing lemma.
Keywords
regularization by noise, fractional Brownian motion,
stochastic sewing, weak existence, local times