Random self-similar trees: dynamical pruning and its applications to inviscid Burgers equations
Episode details
Episode description
Consider the fractional Brownian motions on the real line. What should we expect if we replace the real line by a manifold M? We will provide an answer to this question, extending work begun by Paul Levy in 1965. We will construct a family of Gaussian processes indexed by M with certain properties and argue that these objects are the proper generalization of fractional Brownian motion to the setting of GRF-s over a manifold. We also construct analogs for the Ornstein-Uhlenbeck process indexed by M. After discussing existence, invariance, self-similarity, regularity and Hausdorff dimension, we will give some examples for different manifolds, discuss simulation, and suggest some open problems for future work. See more on this video at https://www.microsoft.com/en-us/research/video/pacific-northwest-probability-seminar-random-self-similar-trees-dynamical-pruning-and-its-applications-to-inviscid-burgers-equations/
Watch also from the same channel
More episodes from this channel
You might be interested in
