Swedish name: Stokastiska processer
This syllabus is valid: 2018-08-20 valid to 2018-08-26 (newer version of the syllabus exists)
Syllabus for courses starting after 2018-08-27
Syllabus for courses starting before 2018-08-26
Course code: 5MS065
Credit points: 7.5
Education level: Second cycle
Main Field of Study and progress level:
Mathematical Statistics: Second cycle, has only first-cycle course/s as entry requirements
Statistics: Second cycle, has only first-cycle course/s as entry requirements
Computational Science and Engineering: Second cycle, has only first-cycle course/s as entry requirements
Grading scale: TH teknisk betygsskala
Responsible department: Department of Mathematics and Mathematical Statistics
Established by: Faculty Board of Science and Technology, 2018-10-04
The course gives an introduction to the theory of stochastic processes, especially Markov processes, and a basis for the use of stochastic processes as models in a great number of fields of application, such as queuing theory, Markov Chain Monte Carlo (MCMC), hidden Markov models (HMM) och financial mathematics. The course also covers simulation of stochastic processes and inference for the models. Furthermore, the course covers discrete Markov chains and Markov processes, the Markov property, Chapman-Kolmogorov's theorem and classification of Markov processes. The notions transition probability, transition intensity, forward- and backward equations, and stationary and asymptotic distributions are defined. The convergence of Markov chains, birth- and death processes, absorption probabilities, absorption times, renewal theory, martingales, and Brownian motion and diffusion are studied. Finally, an introduction to stochastic integration and stochastic differential equations is given.
For a passing grade, the student must be able to
Knowledge and understanding
Skills and abilities
Judgement and approach
The course requires a total of 90 ECTS including a course in Probability Theory on advanced level minimum 7,5 ECTS. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
The teaching is mainly through lectures, problem solving sessions and supervision.
The course is examined by a written exam. For the course, one of the following grades is assigned: Fail (U), Pass (G), Pass with distinction (VG). The grade is decided by the written exam.
A student who has received a passing grade on a test is not allowed to retake the test in order to receive a higher grade. A student who has not received a passing grade after participating in two tests has the right to be assigned another examiner, unless there are certain circumstances prohibiting this (see the Higher Education Ordinance, Chapter 6, 22§). A request to be assigned another examiner should be addressed to the head of department for the department of mathematics and mathematical statistics. The possibility of being examined based on the current version of the syllabus is guaranteed for at least two years following the student's first participation in the course.
Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications
In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.
Stirzaker David
Stochastic processes and models
Oxford : Oxford Univ. Press : 2005 : 331 s. :
ISBN: 0-19-856813-4
Mandatory
Search the University Library catalogue
Markovprocesser
Rydén Tobias , Lindgren Georg
2. uppl. : Lund : Univ. : 2000 : 161 s. :
Mandatory