Topics in Applied Probability:Tempered Stable Distributions, Ad Placement, and Turing's Formula. Lecture 2

Lecture 2: Tempered stable distributions and processes. Abstract: In this lecture we introduce the class of tempered stable distributions, which is a large and flexible class of models with tempered heavy tails. We discuss many properties of these distributions and their associated Levy processes. In particular, we analyze the tails of these distributions and we characterize when their associated Levy processes are close to stable Levy process and when they are close to Brownian motion.