autumn 2024
STA-2001 Stochastic Processes - 10 ECTS

Type of course

The course is mandatory in the study programs Applied Physics and Mathematics - master (5-years) and Mathematical Sciences - Bachelor. It may also be taken independent of study program. This course is also available for inbound exchange students

Admission requirements

Applicants from Nordic countries: Generell studiekompetanse og følgende spesielle opptakskrav: Matematikk R1 + R2 og i tillegg enten:

  • Fysikk 1 + 2 eller
  • Kjemi 1+ 2 eller
  • Biologi 1 + 2 eller
  • Informasjonsteknologi 1 +2 eller
  • Geofag 1 + 2 eller
  • Teknologi og forskningslære 1 + 2

International applicants: Higher Education Entrance Qualification and certified language requirements in English. It is a requirement that students have some prior knowledge of biology and ecology, chemistry and mathematics (Participants must have taken introductory level university courses, and achieved pass grades, in these subjects).

A list of the requirements for the Higher Education Entrance Qualification in Norway can be found on the Norwegian Agency for Quality Assurance in Education website -

Application code: 9336 (Nordic applicants).

Course overlap

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

S-210 Stocastic processes 10 ects

Course content

This course builds on STA-1001 Probability and statistics. The course is a continuation of the probability theory presented in STA-1001 with an emphasis on construction, interpretation and analysis of probability models for simple processes or dynamic systems. Discusses conditional probability, conditional expectations, Markov chains, Poisson processes, branching processes, birth and death processes and other stochastic processes.

Recommended prerequisites

STA-1001 Probability and statistics

Objectives of the course

This course gives students an introduction to applied probability theory and stochastic processes, including use of conditioning as an important tool for probability computations. Within stochastic processes, primary emphasis is placed upon the analysis of models with countable state space in discrete or continuous time. Of special importance is that students have a command of different types of Markov processes, including Poisson processes and birth and death processes.

The student shall:

  • be able to use basic probability theory. Here it is important to be able to do computations with stochastic variables, with one- or multi-dimensional distributions. Special importance is attached to conditional probability and conditional expectation, and to be able to use these as tools in probability computations and stochastic models.
  • be able to set up and analyze Markov models in discrete time. Here it is important to be able to express Markov models by means of transition matrices and to compute the probability for transitions in one or more steps. One must be able to classify states, find expected time in states and limit probabilities for different states. One should also be able to identify and utilize the fact that a process is time-reversible and to be able to analyze the special case of branching processes.
  • have fundamental knowledge of Poisson processes. Here it is important to understand the distribution in time between occurrences, between a given number of occurrences, and conditional distribution of occurrence times. In conjunction with this, the exponential distribution and its properties are important. One should have knowledge of extensions of the Poisson model: non-homogeneous, conditional, and compound Poisson processes.
  • be able to set up and analyze Markov models in continuous time. Here it is important to be able to express models with the help of transition rates, and to find the probability for transition with the help of differential equations. One should also be able to find the limiting probabilities given by balance equations, and be able to recognize and utilize that a process is time-reversible. Special emphasis is given to birth and death processes, including the expected number of individuals, expected time to reach a certain number of individuals, transition probabilities and limiting distributions for these.

Language of instruction and examination

The language of instruction and the syllabus is English. Examination questions will be given in English, but may be answered either in English or a Scandinavian language.

Teaching methods

Lectures: Approx 40 h. Coursework: Approx 30 h.

Information to incoming exchange students

This course is open for inbound exchange student who meets the admission requirements, including prerequisites. Please see the Admission requirements" and the "Prerequisite" sections for more information.

Do you have questions about this course? Please check the following website to contact the course coordinator for exchange students at the faculty:



Examination: Date: Duration: Grade scale:
School exam 12.12.2024 09:00
4 Hours A–E, fail F

Coursework requirements:

To take an examination, the student must have passed the following coursework requirements:

Mandatory homework sets Approved – not approved
UiT Exams homepage

  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: STA-2001
  • Tidligere år og semester for dette emnet