Econometrics: the study of (discrete time) time series.
State spaced models, Generalized Autoregressive Score (GAS) models, also known as Dynamic Conditional Score (DCS) models, optimality criterions for econometric models, realized Kullback-Leibler optimality, Kalman filtering, non-linear filters.
Probability Theory: the most famous subset of measure theory.
Normal approximations, Berry Esseen Bounds, Malliavin operators.