In this thesis we study the $L^p$ Dirichlet problem for second order divergence-form operators having a BMO antisymmetric part. To be precise, for the divergence-form …
This thesis is a large deviations study for the performance of an interacting particle method for rare event estimation. The analysis is restricted to a …
In this dissertation, we mainly discuss two topics of partial differential equations in fluid dynamics and kinetic theory: viscous surface wave and diffusive limit. With …
Large deviations are classical topics of study that enjoy great practical application under probability theory. In essence, it studies the properties lie in the tail …