Chapter 5

Brownian Motion

5.1 Intuitive Introduction to Diffusions

Rating

Mathematically Mature: may contain mathematics beyond calculus with
proofs.

Section Starter Question

Suppose you wanted to display the functiony=

√

xon a graphing calculator.
Describe the process necessary to choose a proper window to display the
graph.

Key Concepts

1. The passage from discrete random walks to continuous stochastic pro-
   cesses, from the probability point of view and the partial differential
   equation point of view.

Vocabulary

1. Adiffusion process, or adiffusionfor short, is a Markov process
   for which all sample functions are continuous. It is also a solution to a
   stochastic differential equation.

155