TAMS45	Stationary Stochastic Processes, ECTS-points /STATIONÄRA STOKASTISKA PROCESSER/ Advancement level: C
	Aim: The course treats theory and methods to handle sequences of observations and continuous registrations where the observations are related. Examples are random models of electronic signals, noise, turbulence, registrations in industrial processes and economical time series. The course is intended as a basis for understanding professional literature in teletransmission theory, control theory, information theory, optimization etc. Prerequisites: Basic courses in mathematical statistics. Theory of analytic functions. Also transform theory is very helpful. Supplementary courses: TAMS50 Applied probability models TSRT35 Control theory TSIT64 Signal theory TBMT11 Biomedical signal processing Course content: Conditioning. Random vectors and the multivariate normal distribution. Examples of stochastic processes and their use. Different process descriptions and questions about existence. Mean and covariance functions, stationarity, convergence and criteria for convergence. Derivatives and integrals of stochastic processes. Methods to simulate stationary sequences. Processes with orthogonal increments. Spectral representations of processes, spectral density, signals in linear nets. Hilbert spaces, the projection theorem, prediction and filtering with explicit solutions for rational spectral density, white noise. Estimation of means, covariance functions and spectral densities. Ergodicity. Practical applications. Course literature: Hjorth, U. :Stokastiska processer, korrelations- och spektralteori. Studentlitteratur. Complementary material published by the department.
TEN1	Written examination

Course language is Swedish.