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: 27.02.2023 - 17.04.2023
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
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language : English
Teaching Period : 2022-2023 Spring IV
2023-2024 No teachingEnrollment :
Sisu (sisu.aalto.fi)