Description: Section I. Finsler Laplacians in Application.- to Diffusions on Finsler Manifolds.- Density Dependent Host/Parasite Systems of Rothschild Type and Finslerian Diffusion.- Stochastic Finsler Geometry in the Theory of Evolution by Symbiosis.- Section II. Stochastic Analysis and Brownian Motion.- Diffusions on Finsler Manifolds.- Stochastic Calculus on Finsler Manifolds and an Application in Biology.- Diffusion on the Tangent and Indicatrix Bundles of a Finsler Manifold.- Section III. Stochastic Lagrange Geometry.- Diffusion on the Total Space of a Vector Bundle.- Diffusions and Laplacians on Lagrange Manifolds.- ?-Lagrange Laplacians.- Section IV. Mean-Value Properties of Harmonic Functions.- Diffusion, Laplacian and Hodge Decomposition on Finsler Spaces.- A Mean-Value Laplacian for Finsler Spaces.- Section V. Analytical Constructions.- The Non-Linear Laplacian for Finsler Manifolds.- A Bochner Vanishing Theorem for Elliptic Complices.- A Lichnerowicz Vanishing Theorem for Finsler Spaces.- A Geometric Inequality and a Weitzenbck Formula for Finsler Surfaces.- Spinors on Finsler Spaces.

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