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) Todays 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 : outcome of random experiment : sample space- set of all possible outcomes A collection, F , of subsets of is a -field (aka -algebra) if: F if A...
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Lec1_0922 - Math136 / Stat219 Course Goals Basic concepts...

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