Current Topics Seminar
| Speaker | Joshua Tokle |
| Title | Markov Processes and PDE |
| Date | October 7 4:00pm PDL C-36 |
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What does the Laplacian have to do with Brownian motion? More generally, what does it mean for a differential operator to be the infinitessimal generator of a Markov process? In this talk I will show how Markov processes can be constructed as probability measures on an appropriate function space and I will develop the connection between Markov processes and PDE. If time permits, I will define a family of processes called $\alpha$-stable processes, a nonlocal operator called the fractional Laplacian, and I will discuss my work in obtaining explicit heat kernel bounds for these objects. This talk may be of interest to students taking Chen's special topics course who don't have a background in stochastic processes.
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