A weak space-time formulation for the linear stochastic heat equation
Preprint, 2014

We apply the well-known Banach-Necas-Babuska inf-sup theory in a stochastic setting to introduce a weak space-time formulation of the linear stochastic heat equation with additive noise. We give sufficient conditions on the the data and on the covariance operator associated to the driving Wiener process, in order to have existence and uniqueness of the solution. We show the relation of the obtained solution to the so-called mild solution and to the variational solution of the same problem. The spatial regularity of the solution is also discussed. Finally, an extension to the case of linear multiplicative noise is presented.

Linear multiplicative noise

Inf-sup theory

Stochastic linear heat equation

Additive noise


Stig Larsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Matteo Molteni

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet




Grundläggande vetenskaper