Regular varying functions are almost power-law functions. And tails of many random variables are regularly varying. It is natural to generalize those notions to stochastic processes. So for the first part of the talk, we will talk about regular variation for multivariate processes with Cadlag paths. Then I will explain why extremal behavior of such processes are often due to the (single) largest jump. Extremal behaviors are closely related to heavy-tailed large deviation principle on the space of Cadlag functions, which are the topics for the second part of the talk. Heavy-tailed LDPs are helpful to study functionals of partial sum processes. For example, ruin probabilities and long strange segments. The applications again reflect the idea that the largest jump determines the extremal behaviors.

Everyone is welcome. No background knowledge is assumed, though knowledge of probability theory are helpful.