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A decomposition of Bessel bridges

Joonyong Choi
Monday, October 19, 2020 - 2:30pm to 3:30pm

In the third sequence of the hidden gems seminar, we’re going to discuss Bessel processes and Bessel bridges which are perhaps the most important continuous stochastic processes next to Brownian motions. In fact, various Brownian functionals such as a standard excursion and local times are described by Bessel processes and their bridges. The squares of Bessel processes are additive processes and frequently appear as limits of population genetic models and branching processes. We’re going to take a look at a universal representation of the law of any squared Bessel processes. We’ll also going to discuss a remarkable result that any Bessel bridge can be written as a sum of four independent pieces of other kinds of Bessel bridges. This talk is based on the eponymous paper by Jim Pitman and Marc Yor from 1982. 

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