A weak space-time formulation for the linear stochastic heat equation
Journal article, 2017

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

Additive noise

Linear multiplicative noise

Stochastic linear heat equation

Author

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Matteo Molteni

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

International Journal of Applied and Computational Mathematics

2199-5796 (eISSN)

Vol. 3 2 787-806

Subject Categories

Mathematics

Computational Mathematics

Probability Theory and Statistics

Roots

Basic sciences

DOI

10.1007/s40819-016-0134-2

More information

Latest update

11/25/2019