Stationary Stochastic Processes
Stationära stokastiska processer

FMSF10F, 7.5 högskolepoäng

Gäller från och med: Autumn 2020
Beslutad av: Anders Gustafsson / FUN
Datum för fastställande: 2020-05-18

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSF10
Undervisningsspråk: English

Syfte

The student shall aquire a toolbox containing concepts and models for description and handling of stationary stochastic processes within many different areas, such as, signal processing, automatic control, information theory, economics, biology, chemistry, and medicine. The mathematical and statistical elements are therefore illustrated using a wide variety of examples from different areas of application. The course shall also give the student the ability to identify the presence of stationary processes in other courses in the education, use the knowledge of stationary processes in other courses, and translate the concepts and tools between different courses, building on stationary processes.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• be able to perform calculations using expectations, variance, covariance, and cross-covariance within and between different stationary processes,
• be able to calculate the relationship between covariance properties in the timedomain and spectral properties in the frequency domain for one and several processes,
• be able to formulate linear filters using covariance and spectral properties,
• be able to estimate covariance function, spectrum, and other parameters in stationary processes using data.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• be able to identify natural situations where a stationary process is a suitable mathematical model, e.g., within at least one engineering, science, or economics application,
• be able to formulate a stationary stochastic process model using a concrete problem within the chosen application,
• be able to suggest model parameters, with the help of data,
• be able to interpret the model and translate model concepts to a conclusion regarding the original problem.

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden

• be able to read and interpret technical literature with elements of stationary processes within the chosen application,
• be able to describe the model structure and the conclusions,
• be able to describe the possibilities and limitations of stochastic models.

Kursinnehåll

Models for stochastic dependence. Concepts of description of stationary stochastic processes in the time domain: expectation, covariance, and cross-covariance functions. Concepts of description of stationary stochastic processes in the frequency domain: power spectrum, cross spectrum. Special processes: Gaussian process, Wiener process, white noise, Gaussian fields in time and space. Stochastic processes in linear filters: relationships between in- and out-signals, auto regression and moving average (AR, MA, ARMA), derivation and integration of stochastic processes. The basics in statistical signal processing: estimation of expectations, covariance function, and spectrum. Application of linear filters: frequency analysis and optimal filters.

Kurslitteratur

Lindgren, G., Rootzén, H., Sandsten & M.: Introduction to Stationary Stochastic Processes: Applications in Science and Engineering.. Chapman & Hall, 2013. ISBN 9781466586185.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar

Kursens examination

Examinationsform: Skriftlig tentamen
Betygsskala: Underkänd, godkänd
Examinator: Professor Maria Sandsten

Antagningsuppgifter

Förutsatta förkunskaper: A basic course in mathematical statistics and knowledge in complex and linear analysis.

Kurstillfällesinformation

Startdatum: 2020-08-31
Slutdatum: 2020-10-30
Kursfart: Half time

Kontaktinformation och övrigt

Kursansvarig: Maria Sandsten <maria.sandsten@matstat.lu.se>
Hemsida: http://www.maths.lu.se/kurshemsida/fmsf10masc04/