  Motivated by applications, we introduce a general and new framework for
operator valued positive definite kernels. We further give applications both to
operator theory and to stochastic processes. The first one yields several
dilation constructions in operator theory, and the second to general classes of
stochastic processes. For the latter, we apply our operator valued
kernel-results in order to build new Hilbert space-valued Gaussian processes,
and to analyze their structures of covariance configurations.
