MS-E1604 - Brownian motion and stochastic analysis D, Lecture, 24.2.2025-7.4.2025

Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

LEARNING OUTCOMES

Upon completing the course, the student

1. is familiar with the basic concepts of stochastic analysis, such as martingales, stopping times, optional sampling, Brownian motion, and stochastic integral, and is aware of their underlying assumptions,

2. can apply martingale theory and the basics of stochastic integral to modeling and analyzing random phenomena,

3. is prepared to extend his/her knowledge to more sophisticated theory and techniques, for example by using the scientific literature in the field.

Credits: 5

Schedule: 24.02.2025 - 07.04.2025

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Eveliina Peltola

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

  • valid for whole curriculum period:

    Brownian motion is a fundamentally important stochastic process, discovered in the contexts of financial markets and statistical physics. It relates to diverse mathematical topics from partial differential equations to constructive quantum field theory. This course introduces you to the key techniques for working with Brownian motion, including stochastic integration, martingales, and Ito's formula. 

Assessment Methods and Criteria

  • valid for whole curriculum period:

    Exam and homework

Workload

  • valid for whole curriculum period:

    Attending lectures 24h

    Attending exercise classes 12h

    Solving exercises 68-97h

    Attending and preparing for the exam 2-32h

DETAILS

Study Material

  • valid for whole curriculum period:

    • E Peltola. Brownian Motion and Stochastic Analysis. Lecture notes.
    • N Berestycki. Stochastic Calculus and Applications. Lecture notes, 2010.
    • JF Le Gall. Brownian Motion, Martingales, and Stochastic Calculus. Graduate Texts in Mathematics, volume 274, 2016.
    • R Durrett. Stochastic calculus: a practical introduction. CRC  Press, Probability and Stochastics Series, 1996.

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Teaching Language: English

    Teaching Period: 2024-2025 Spring IV
    2025-2026 No teaching

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