Brownian Motion on Finsler Manifolds
Definition and Existence
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The aim of this thesis is to extend the concept of Brownian motion on Riemannian manifolds to the more general Finsler manifolds. We give a reasonable definition of Brownian motion which is very similar to the one in the Riemannian case. However for the proof of existence we use a slightly different but equivalent approach to Brownian motion. Therefore we introduce the Finsler Laplacian in a natural way and apply the Moreau-Yosida approximation and the theory of nonpositively curved metric spaces to construct a global solution to the heat equation on Finsler manifolds. Furthermore we approxima...
The aim of this thesis is to extend the concept of Brownian motion on Riemannian manifolds to the more general Finsler manifolds. We give a reasonable definition of Brownian motion which is very similar to the one in the Riemannian case. However for the proof of existence we use a slightly different but equivalent approach to Brownian motion. Therefore we introduce the Finsler Laplacian in a natural way and apply the Moreau-Yosida approximation and the theory of nonpositively curved metric spaces to construct a global solution to the heat equation on Finsler manifolds. Furthermore we approximate the Finsler structure by a time-dependent Riemannian metric which is induced by a function on the manifold. Aside from that we apply the recently proven existence theorem for Brownian motion on time-dependent Riemannian manifolds.
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