Stochastic Processes: Generation and Embedding

This lecture covers the generation of stochastic processes, focusing on stationary Gaussian processes, discrete time Markov processes, continuous time - discrete state Markov processes, Poisson processes, and circulant embedding. The instructor explains the concepts of weakly and strongly stationary Gaussian processes, as well as the circulant embedding of matrices. The lecture also discusses the generation of processes on a uniform grid and the diagonalization of circulant matrices using the Fourier matrix. Various algorithms and properties related to circulant embedding are presented, along with practical examples and possible remedies for non-positive definite matrices.