  The purpose of this work is to extend the formalism of stochastic calculus to
the case of spaces with local anisotropy (modeled as vector bundles with
compatible nonlinear and distinguished connections and metric structures and
containing as particular cases different variants of Kaluza--Klein and
generalized Lagrange and Finsler spaces). We shall examine nondegenerate
diffusions on the mentioned spaces and theirs horizontal lifts.
