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Lec1_0922

# Lec1_0922 - Math136 Stat219 Course Goals • Basic concepts...

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Unformatted text preview: Math136 / Stat219 Course Goals • Basic concepts and definitions of measure-theoretic probability and stochastic processes • Properties of key stochastic processes and their applications, especially Brownian motion • Key results and common techniques of proof • Preparation for further study (especially for Math 236: stochastic differential equations) Today’s lecture: Sections 1.1 MATH136/STAT219 Lecture 1, September 22, 2008 – p. 1/7 Why Measure-Theoretic Probability? • Mathematical models of physical processes • Outcome is uncertain or “random” • Probability = “Language” • Measure Theory = “Grammar” • Measure theory allows us to consider ◦ General random variables ◦ Arbitrary probability spaces MATH136/STAT219 Lecture 1, September 22, 2008 – p. 2/7 Measurable space • ω : outcome of random experiment • Ω : sample space- set of all possible outcomes • A collection, F , of subsets of Ω is a σ-field (aka σ-algebra) if: ◦ Ω ∈ F ◦ if A...
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Lec1_0922 - Math136 Stat219 Course Goals • Basic concepts...

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