A weak space-time formulation for the linear stochastic heat equation
Artikel i vetenskaplig tidskrift, 2016

We apply the well-known Banach–Nečas–Babuška 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 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 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.

Inf–sup theory

Stochastic linear heat equation

Additive noise

Linear multiplicative noise

Författare

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Matteo Molteni

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

International Journal of Applied and Computational Mathematics

2199-5796 (eISSN)

Vol. Epub ahead of print

Ämneskategorier

Matematik

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper

DOI

10.1007/s40819-016-0134-2