  We construct p-adic Euclidean random fields {\Phi} over Q_{p}^{N}, for
arbitrary N, these fields are solutions of p-adic stochastic pseudodifferential
equations. From a mathematical perspective, the Euclidean fields are
generalized stochastic processes parametrized by functions belonging to a
nuclear countably Hilbert space, these spaces are introduced in this article,
in addition, the Euclidean fields are invariant under the action of certain
group of transformations. We also study the Schwinger functions of {\Phi}.
