Applied Mathematics Colloquium
Tuesday,
October 23, 2018
2:45 PM - 3:45 PM
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Nawaf Bou-Rabee, Rutgers
Title:
Sticky Diffusions & their Numerical Solution
Abstract:
Feller's boundary condition for Brownian motion extends the classical Dirichlet, Neumann and Robin conditions -- corresponding to killed, reflecting and elastic Brownian motions, respectively -- to second-order derivative boundary conditions which give rise to `sticky' boundary behavior. In this talk, we revisit Brownian motions with Feller's boundary condition, and show, for the first time, how to capture their dynamics using a simple modification of the random walk approximation of Brownian motion. We then generalize this result to high-dimensional sticky diffusion processes. Our approximation turns out to be thousands of times faster than a penalty method.
This approximation builds on ideas in “Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations”, AMS Memoir, ISBN: 978-1-4704-3181-5. The talk itself is based on a forthcoming paper with Miranda Holmes-Cerfon.
Nawaf Bou-Rabee, Rutgers
Title:
Sticky Diffusions & their Numerical Solution
Abstract:
Feller's boundary condition for Brownian motion extends the classical Dirichlet, Neumann and Robin conditions -- corresponding to killed, reflecting and elastic Brownian motions, respectively -- to second-order derivative boundary conditions which give rise to `sticky' boundary behavior. In this talk, we revisit Brownian motions with Feller's boundary condition, and show, for the first time, how to capture their dynamics using a simple modification of the random walk approximation of Brownian motion. We then generalize this result to high-dimensional sticky diffusion processes. Our approximation turns out to be thousands of times faster than a penalty method.
This approximation builds on ideas in “Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations”, AMS Memoir, ISBN: 978-1-4704-3181-5. The talk itself is based on a forthcoming paper with Miranda Holmes-Cerfon.
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