Multiplicative stochastic heat equations on the whole space

Abstract

We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on ${\mathbf{R}}^3$, and on the other hand the KPZ equation on $\mathbf{R}$ via the Cole-Hopf transform. To perform these constructions, we adapt the theory of regularity structures to the setting of weighted Besov spaces. One particular feature of our construction is that it allows one to start both equations from a Dirac mass at the initial time.

52 pages

Cited by in corpus (18)

• Global solutions to elliptic and parabolic ${\Phi }^4$ models in Euclidean space
• The continuous Anderson hamiltonian in $d\le 3$
• The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher
• Discretisation of regularity structures
• KPZ equation limit of sticky Brownian motion
• An averaged space-time discretization of the stochastic $p$-Laplace system
• Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise
• Stochastic Analysis with Modelled Distributions
• Construction of a non-Gaussian and rotation-invariant ${\Phi }^4$-measure and associated flow on ${\mathbb{R}}^3$ through stochastic quantization
• Stochastic PDE limit of the dynamic ASEP
• Solving McKean-Vlasov SDEs via relative entropy
• KPZ fluctuations in the planar stochastic heat equation
• Singular SPDEs on Homogeneous Lie Groups
• BPHZ renormalisation and vanishing subcriticality asymptotics of the fractional ${\Phi }_d^3$ model
• The continuum parabolic Anderson model with a half-Laplacian and periodic noise
• Anderson Hamiltonians with singular potentials
• A nonlinear Strassen law for singular SPDEs
• Construction and spectrum of the Anderson Hamiltonian with white noise potential on ${\mathbf{R}}^2$ and ${\mathbf{R}}^3$