Paul Albert Besold
Solutions to Stochastic Partial Differential Equations as Elements of Tensor Product Spaces
Preprint series: Mathematica Gottingensis
MSC:
60H15 Stochastic partial differential equations, See also {35R60}
35R60 Partial differential equations with randomness, See Also {
Abstract: Stochastic partial differential equations of elliptic type
are investigated. Stochastic partial differential operators
with deterministic coefficients can be understood as the
tensor product of a partial differential operator defined
on the Sobolev Spaces on $\R^d$ with an appropriate operator
on the Hida distribution spaces, the operator being defined
on the topological tensor product of these spaces. Operators
with random coefficients are also interpreted as operators
on such spaces. Criterion for the existence and uniqueness
of solutions in this framework are established.
Keywords: Stochastic partial differential equations, Hida Spaces, Tensor Products of Distribution Spaces, Stochastic distributions and test functions