Statistics and Mathematics colloquium: Geodesic random walks, diffusion processes, and Brownian motion on Finsler manifolds

Event status:

You are welcome to attend the following joint Statistics and Mathematics colloquium (part of the Colloquium Series of the Department of Mathematical and Physical Sciences) at La Trobe University organised together with the PVSeminar

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Date:
Thursday 11 May 2023 05:00 pm until Thursday 11 May 2023 06:00 pm (Add to calendar)
Contact:
Andriy Olenko
a.olenko@latrobe.edu.au
Presented by:
Vladimir S. Matveev
Type of Event:
Public
Cost:
Free

We show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.

In particular, the generator of the limit process is a non-degenerate elliptic second-order partial differential operator for which we give a precise integral formula.

If the geodesic random walk is geometric, that is if the law of increments are constructed by the Finsler metric by a coordinate-invariant procedure, the Riemannian metric is then determined by the Finsler metric.

Special cases of such functors  F →  g_F include the Binet-Legendre metric and different average metrics and has many effective applications in Finsler geometry in which in particular certain mathematicians from the La Trobe University are involved.

Also possible applications in natural and life sciences will be discussed.

Most results are joint with Tianyu Ma and Ilya Pavlyukevich.

A PDF file with the talk slides (if any) might become available for downloading from the Webpage at https://probvic.wordpress.com/pvseminar/ prior to the talk.

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