Advanced Probability

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Author(s): M. Lis, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2017

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; statistics; probability; stats; stat

Introduction
Some measure theory
Review of measure theory
Conditional expectation
Martingales in discrete time
Filtrations and martingales
Stopping time and optimal stopping
Martingale convergence theorems
Applications of martingales
Continuous time stochastic processes
Weak convergence of measures
Brownian motion
Basic properties of Brownian motion
Harmonic functions and Brownian motion
Transience and recurrence
Donsker's invariance principle
Large deviations
Index