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ST 747 Probability and Stochastic Processes II
Advanced development of stochastic processes. Conditional expectation, filtrations of sigma-algebras, stopping times. Martingales, associated convergence theorems and inequalities, martingale decomposition, optional stopping. Markov chains including random walks, recurrence versus transience, asymptotic behavior. General Markov processes and the related semigroup operators. Construction and properties of Brownian motion, Donsker's invariance principle. Other potential topics include stationary processes, Birkhoff's ergodic theorem, branching processes, Poisson processes.
Prerequisite: MA(ST) 546
Typically offered in Spring only
Statistics (PhD)
/graduate/sciences/statistics/statistics-phd/
1 Unless student has taken ST聽542 Statistical Practice 2 A 500-level or 700-level course in either statistics or another department with material relevant to the student鈥檚 plan of work. Examples include ST聽520 , ST聽531 , ST聽533 , ST聽534 , ST聽537 , ST聽540 , ST聽544 , ST聽546 / MA聽546 , ST聽563 , ST聽721 ,聽 ST聽732 , ST聽733 , ST聽740 , ST聽745 , ST聽746 , ST聽747 / 惭础听747 , and聽 ST聽790 3 Additional courses may include聽 ST聽801 ,聽 ST聽895 聽and courses taken from a Master of Statistics or Master of Science in Statistics degree at NCSU.