# Rearranged Stochastic Heat Equation

@inproceedings{Delarue2022RearrangedSH, title={Rearranged Stochastic Heat Equation}, author={Franccois Delarue and William R.P. Hammersley}, year={2022} }

The purpose of this work is to provide an explicit construction of a strong Feller semigroup on the space of probability measures over the real line that additionally maps bounded measurable functions into Lipschitz continuous functions, with a Lipschitz constant that blows up in an integrable manner in small time. Our construction relies on a rearranged version of the stochastic heat equation on the circle driven by a coloured noise. Formally, this stochastic equation writes as a reflected…

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