AMATH 677Stochastic Processes for Applied Mathematics

Random variables, expectations, conditional probabilities, conditional expectations, convergence of a sequence of random variables, limit theorems, minimum mean square error estimation, the orthogonality principle, random process, discrete-time and continuous-time Markov chains and applications, forward and backward equation, invariant distribution, Gaussian process and Brownian motion, expectation maximization algorithm, linear discrete stochastic equations, linear innovation sequences, Kalman filter, various applications. (Held with AMATH 477. Students in AMATH 677 will be expected to meet some additional learning objectives.)