Kaj Nyström: The Skorohod Oblique Reflection Problem in Time-dependent Domains

The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form discussed in this talk, the multi-dimensional Skorohod problem was introduced, in time-independent domains, by H. Tanaka and further investigated by P.-L. Lions and A.-S. Sznitman. Subsequent results of several researchers have resulted in a large literature on the Skorohod problem in time-independent domains. In a recent paper (joint work with T. Önskog) we conduct a thorough study of the multi-dimensional Skorohod problem in time-dependent domains, and we subsequently use the established results to construct solutions to stochastic differential equations with oblique reflection in time-dependent domains. The purpose of the talk is to briefly discuss these results.