  In this study, we consider weighted stochastic field exponent function spaces
$L_{\vartheta }^{p(.,.)}\left( D\times \Omega \right) $ and $W_{\vartheta
}^{k,p(.,.)}\left( D\times \Omega \right) $. Also, we investigate some basic
properties and embeddings of these spaces. Finally, we present an application
of these spaces to the stochastic partial differential equations with
stochastic field growth.
