Probability II

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Typical Scheduling: 
Every spring semester

Develops the probability basis requisite in modern statistical theories and stochastic processes. (2nd of two courses)


MATH 6241 or equivalent

Course Text: 

At the level of Billingsley:  Probability and Measure

Topic Outline: 
  • Characterizations and limit theorems for sums of independent random variables, such as extensions and/or error analysis for central limit theorems, the iterated law of large numbers, properties of infinitely divisible distributions, and tail events, symmetric events and zero-one laws
  • Random walks, including basic properties and recurrence results
  • Conditional probability and conditional expectation, including basic properties and connections to Radon-Nikodym derivatives, projections, etc.
  • Markov processes, including basic properties and examples, stopping times and the strong Markov property, use of transition probabilities, and applications
  • Martingales, including basic inequalities and convergence theorems, optional sampling, backward martingales, and applications
  • Ergodic theory, including basic definitions and examples, and topics such as the Pointwise Ergodic Theorem, recurrence and mixing
  • Poisson processes and Brownian motion, including basic constructions and some basic properties