Abstract We consider the stochastic reaction–diffusion equation in 1+1 1 + 1 dimensions driven by multiplicative space–time white noise, with a distributional drift belonging to a Besov–Hölder space with any regularity index strictly larger than -1 - 1. We assume that the diffusion coefficient is a regular function which is bounded away from zero. By using a combination of stochastic sewing techniques and Malliavin calculus, we show that the equation admits a unique solution.
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Konstantinos Dareiotis
Teodor Holland
Khoa Lê
Probability Theory and Related Fields
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Dareiotis et al. (Sat,) studied this question.
www.synapsesocial.com/papers/69ada8dfbc08abd80d5bc39c — DOI: https://doi.org/10.1007/s00440-026-01474-0