• Corpus ID: 252693379

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… 

References

SHOWING 1-10 OF 80 REFERENCES

Stochastic McKean-Vlasov equations

We prove the existence and uniqueness of solution to the nonlinear local martingale problems for a large class of infinite systems of interacting diffusions. These systems, which we call the

Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection

Abstract. We consider the law ν of the Bessel Bridge of dimension 3 on the convex set K0 of continuous non-negative paths on [0,1]. We prove an integration by parts formula on K0 w.r.t. to ν, where

Weak solutions to the master equation of potential mean field games

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general

The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei

A new approach for the construction of a Wasserstein diffusion

We propose in this paper a construction of a diffusion process on the Wasserstein space P\_2(R) of probability measures with a second-order moment. This process was introduced in several papers by

On directional derivatives of Skorokhod maps in convex polyhedral domains

The study of both sensitivity analysis and differentiability of the stochastic flow of a reflected process in a convex polyhedral domain is challenging because the dynamics are discontinuous at the

Uniqueness and regularity for a system of interacting Bessel processes via the Muckenhoupt condition

We study the regularity of a diusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and

White noise driven SPDEs with reflection

SummaryWe study reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by space-time white noise. The nonlinearity appears both in

Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II

Here A :D(A) ⊂H →H is a self-adjoint operator, K = {x ∈H :g(x) ≤ 1}, where g :H→ R is convex and of class C∞, NK(x) is the normal cone to K at x and W (t) is a cylindrical Wiener process in H (see

A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS

  • 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
...