Course syllabus for Stochastic processes

The course syllabus contains changes
See changes

Course syllabus adopted 2025-12-16 by Head of Programme (or corresponding).

Overview

  • Swedish nameStokastiska processer
  • CodeMVE330
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20144
  • Open for exchange studentsNo

Credit distribution

0109 Examination 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

Go to coursepage (Opens in new tab)

Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

One of the courses:
MVE140 Foundations of probability theory
TMS110 Markov theory
MVE170 Basic Stochastic Processes
TMS125 Basic Stochastic Processes F
MVE135 Random Processes with Applications
Or a similar background: Contact the examinator for more information.

Aim

The course gives a solid knowledge of stochastic processes, intended to be sufficient for applications in mathematical sciences as well as natural sciences, at all levels. An advanced treatment of the theory of stochastic processes relies on probability theory and mathematical analysis. The purpose of the course is to give such a treatment. This means that there is a certain focus on proofs and rigor.

Learning outcomes (after completion of the course the student should be able to)

On successful completion of the course the student will be able to:
  • Define and explain the fundamental concepts of probability theory.
  • Define the most important modes of convergence for sequences of random variables, and explain how they relate to each other.
  • Prove the existence of conditional expectation and compute it in concrete examples
  • Define, provide examples of, and solve problems about martingales in discrete time
  • Prove the most important convergence theorems for martingales in discrete time.
  • Prove and explain the ergodic theorem for stationary processes.
  • Prove and apply de Finetti's theorem.

Content

Fundamentals of probability theory: sigma-algebras and probability measures. Modes of convergence for sequences of random variables. Conditional expectation. Martingales in discrete time, including convergence theorems. Stationary processes and ergodic theory. Random walk. Exchangeable processes.

Organisation

Lectures.

Literature

R. Durrett. Probability: theory and examples, 5th ed

Examination including compulsory elements

Home assignments and/or a written final exam.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.

The course syllabus contains changes

  • Changes to course:
    • 2025-12-16: Content Content changed by PA
      Updated content, from: Stationarity and weak stationarity. Gaussian processes. Renewal theory and queues.Martingales. to:
    • 2025-12-16: Learning outcomes Learning outcomes changed by PA
      Updated information about learning objectives
    • 2025-12-16: Litterature Litterature changed by PA
      Updated literature, from: Grimmett G. and Stirzaker D.: Probability and Random Processes, Third Edition 2001. Chapters 6 and 8-12. To: R. Durrett. Probability: theory and examples, 5th ed
    • 2025-12-16: Organization Organization changed by PA
      Updated organization, from Lectures. Reading assignments. To: Lectures.
    • 2025-12-16: Examination Examination changed by PA
      Updated information about examination, changed from: Home assignments and/or a written final exam. To: Home assignments and/or a written final exam.