Detaljer för kursplan för kurs FMS010F giltig från och med VT 2013 Utskriftsvänlig visning Kurskod:FMS010F Gäller från och med:Vårterminen 2013 Kursplanen är fastställd Allmänt Undervisningsspråk:Engelska Ges:Vid tillräcklig efterfrågan Intresseanmälan:Anmäl intresse via e-post Kurshemsida: Syfte The aim of the course is to increase the understanding of the basic principles and results in the theory of stationary stochastic processes and to add to the arsenal of useful tools for their application. The course givea increased knowledge and skills in stationary stochastic processes on top of basic courses in the subject in the engineering programs: to present and train how stationary process models are constructed and how their mathematical, probabilistic, and statistical properties can be analysed. It is intended as a "second course" in stationary processes; some previous knowledge from mathematical statistics or signal processing helps. Innehåll 1. How to define a stochastic process; sample space, ensemble, distribution 2. Analytic properties of sample functions 3. Covariance function and its spectral representation 4. Spectral representation of a stationary process 5. Linear filters and their spectral properties, white noise 6. Hilbert transform, envelope, Karhunen-Loève expansion 7. Classical ergodic theory, mixing conditions 8. Multivariate processes and cross-correlation properties 9. Spectral properties of random fields 10. Level crossings, extremes and excursions Kunskap och förståelse För godkänd kurs skall doktoranden Know and understand: how to define a stochastic process from finite-dimensional distributions, conditions for different analytical properties, relation between covariance function and spectrum, sprectral representation of a stationary process and its role in linear filters, sampling of stationary process, envelope, statistical formulations of ergodicity, models for random fields, Rice formula Färdighet och förmåga För godkänd kurs skall doktoranden Relate covariance function to spectrum and find continuity and differentiability properties from covariance and spectrum; use the spectral representation of the process to derive filter properties and other relations; use Rice's formula to evaluate extremal- and crossings properties Värderingsförmåga och förhållningssätt För godkänd kurs skall doktoranden Find suitable process models for specific scientific and engineering applications; understand limitations of stationary models; interpret high frequency and low frequency parts of a spectrum in terms of smoothness and long range dependence Undervisningsformer Föreläsningar övningar Examinationsformer Skriftlig tentamen Muntlig tentamen Inlämningsuppgifter Betygsskala:Underkänd, godkänd Förkunskapskrav Förutsatta förkunskaper Introduction to Stationary stochastic processes corresponding to FMSF10 or similar. Urvalskriterier Litteratur Litteratur:Lindgren, G.: Stationary Stochastic Processes: Theory and Applications. Chapman & Hall/CRC, 2012. ISBN 9781466557796. Övrig information The course is a modernized version of a PhD course with the same title that has been given regularly since 2000. Kurskod Kurskod:FMS010F Administrativ information Datum för fastställande: -05-21 Beslutad av:FN1/Anders Gustafsson Alla publicerade kurstillfällen för kursplanen Inga matchande kurstillfällen hittades. 0 kurstillfällen. Utskriftsvänlig visning