Probability Theory and Stochastic Processes with Applications

Chapter 1-2 of this text covers material of a basic probability course. Chapter 3 deals with discrete stochastic processes including Martingale theory. Chapter 4 covers continous time stochastic processes like Brownian motion and stochastic differential equations. The last chapter selected topics got considerably extended in the summer of 2006. In the original course, only localization and percolation problems were included. Now, more topic like estimation theory, Vlasov dynamics, multi-dimensional moment problems, random maps, circle-valued random variables, the geometry of numbers, Diophantine equations and harmonic analysis have been added. No previous knowledge in probability are necessary, but a basic exposure to calculus and linear algebra is required. Some real analysis as well as some background in topology, functional analysis and harmonic analysis can be helpful for the later chapters.