• Corpus ID: 252693379

Rearranged Stochastic Heat Equation

  title={Rearranged Stochastic Heat Equation},
  author={Franccois Delarue and William R.P. Hammersley},
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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  • H. McKean
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1966
Introduction.-The familiar connection between the Brownian motion and the differential operator f -> f"/2, based upon the fact that the Brownian transition function (27rt)-1' exp[-(b a)2/2t] is also