Stochastic Processes and Diffusion on Spaces with Local Anisotropy

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.