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Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - RTG1845

"Diffusions with reflection"

Topic II: Multidimensional reflecting SDEs

 

  1. Definition of reflecting SDE in a domain with a smooth boundary. Example: Brownian motion on a half plane (skew reflection).

  2. Existence and uniqueness theorems.

    • Equations in a halt-space with normal reflection.

    • Localization. General case (partial proofs).

  3. Equations in non-smooth domains.

    • Definition

    • Exterior sphere conditions. Existence and uniqueness theorem. (Ideas, partial proofs).

    • Brownian motion in a wedge. Accessibility of a vertex.