Introduction to Stochastic Processes with Applications in the Biosciences Summary: Introduction to Stochastic Processes with Applications in the Biosciences David F. Anderson University of Wisconsin at Madison Copyright c 2011 by David F. Anderson. Contents 1 Introduction and Review of Background Material 4 1.1 Stochastic Versus Deterministic Models . . . . . . . . . . . . . . . . . 5 1.2 A Review of Linear Differential and Difference Equations . . . . . . . 9 1.2.1 Linear differential equations . . . . . . . . . . . . . . . . . . . 9 1.2.2 Linear Difference Equations . . . . . . . . . . . . . . . . . . . 11 1.3 Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 A Quick Review of Probability Theory 16 2.1 The Probability Space . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 The sample space . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.2 The collection of events F . . . . . . . . . . . . . . . . . . . . 17 2.1.3 The probability measure P . . . . . . . . . . . . . . . . . . . . 18 2.2 Conditional Probability and Independence . . . . . . . . . . . . . . . 19 2.3 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Collections: Mathematics