**MSC:**- 60H15 Stochastic partial differential equations, See also {35R60}
- 35R60 Partial differential equations with randomness, See Also {

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.