Elements of Stochastic Processes

A guiding principle was to be as rigorous as possible without the use of measure theory. Some of the topics contained herein are:

· Fundamental limit theorems such as the weak and strong laws of large numbers, the central limit theorem, as well as the monotone, dominated, and bounded convergence theorems

· Markov chains with finitely many states

· Random walks on Z, Z2 and Z3

· Arrival processes and Poisson point processes

· Brownian motion, including basic properties of Brownian paths such as continuity but lack of differentiability

· An introductory look at stochastic calculus including a version of Ito’s formula with applications to finance, and a development of the Ornstein-Uhlenbeck process with an application to economics