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Regularisation by multiplicative noise for reaction–diffusion equations

Konstantinos Dareiotis et al.

Probability Theory and Related Fields2026https://doi.org/10.1007/s00440-026-01474-0article
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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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https://doi.org/https://doi.org/10.1007/s00440-026-01474-0

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@article{konstantinos2026,
  title        = {{Regularisation by multiplicative noise for reaction–diffusion equations}},
  author       = {Konstantinos Dareiotis et al.},
  journal      = {Probability Theory and Related Fields},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1007/s00440-026-01474-0},
}

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Regularisation by multiplicative noise for reaction–diffusion equations

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