Teaching plan for the course unit



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General information


Course unit name: Stochastic Calculus

Course unit code: 568191

Academic year: 2021-2022

Coordinator: Marta Sanz Sole

Department: Department of Mathematics and Computer Science

Credits: 6

Single program: S

More information enllaƧ



Estimated learning time

Total number of hours 150


Face-to-face and/or online activities



-  Lecture





(Subject to the University regulations due to the Covid disruption.)


-  Lecture with practical component





(Subject to the University regulations due to the Covid disruption.)

Supervised project


Independent learning






Basic notions of real analysis and measure theory, advanced probability, and ordinary differential equations are strongly recommended



Competences to be gained during study



The course aims at developing skills to provide a background and create opportunities to carry out a rigorous analysis of theoretical and practical problems under uncertainty conditions.


Essential training to undertake supervised academic research and also to work in multi-disciplinary environments will be given. This includes not only learning new mathematical topics, but also the access and efficient use of scientific literature, increasing the understanding of rigorous mathematical arguments, developing communication skills, and the capacity of sharing ideas in the professional life.






Learning objectives


Referring to knowledge

To provide an overview on:
— the fundamental results on continuous time stochastic processes, with special emphasis on Brownian motion;
— the Itô’s stochastic calculus and its applications in stochastic modelling.



Teaching blocks


1. A review of basic facts in probability theory and stochastic processes

2. Brownian motion

3. Stochastic integration with respect to the Brownian motion

4. Stochastic differential equations driven by a Brownian motion



Teaching methods and general organization


There will be lectures where the theory will be developed, and joint discussions on exercises assigned to the students.

A manuscript of the course with exercises and their solutions, along with the slides of the lectures will be available.





Official assessment of learning outcomes


There will be two partial exams on week 7 and week 13 (dates are to be fixed) consisting in solving exercises, similar to those discussed in the lectures (65%), and theoretical questions (35%). The final mark will be the arithmetic mean of both. 

Depending on the number of students, at the end of the semester, we will organise sessions with presentations of selected topics by students, and this will count in the final mark. Further details will be given at the beginning of the semester.





Examination-based assessment

The grade will be obtained with a final examination consisting of theoretical questions (35%) and problems (65%). To pass the exam, the requirement of reaching a score of 4/10 on the theory questions will apply.