Exam dates:

Please check this this the day before the exam. There may be minor changes.

• December 3
  • Place: seminar room 822, SBII
  • 09:00-09:40 - Isak Hammer
  • 09:45-10:25 - Daniel Kjellevold Steinsland
  • 10:30-11:10 - Nora Røhnebæk Aasen
  • Break
  • 11:45-12:25 - Simen Knutsen Furset
  • 12:30-13:10 - Even Aslaksen
  • Break
  • 13:30-14:10 - Diego Caudillo
  • 14:15-14:55 - Martin Ludvigsen

• December 14:
  • Place: seminar room 656, SBII.
  • 09:00-09:40 - Daniel Ørnes Halvorsen
  • 09:45-10:25 - Tor Ola Solheim
  • 10:30-11:10 - Sjur Bergmann
  • Break
  • 11:45-12:25 - Thomas Christiansen
  • 12:30-13:10 - Ekaterina Poliakova
  • Break
  • 13:30-14:10 - Marco Biemann
  • 14:15-14:55 - Ludwig Rahm

Each exam takes 40 minutes.

Prepare for:

• Ca. 10 minutes presentation of your project. If you are using slides, send them to anne [dot] kvarno [at] ntnu [dot] no the day before the exam.
• Ca. 10 minutes presentation (on the blackboard, do not use slides for this) of one of the topics listed below.
  • You are supposed to prepare for all of them.
  • Be efficient: write the mathematics on the blackboard, and explain it orally.
  • You are allowed to bring with you a sheet of paper with some key-words for the presentation.
  • Your selected (or rather drawn) topic will be sent you ca. 40 minutes before your exam starts.
• The rest of the time will be used for more detailed questions about the topics above, and questions from other part of the curriculum.

List of topics to prepare a short presentation about:

• Construction of an Ito integral
• Ito’s formula
• SDEs, existence and uniqueness results
• Milstein’s fundamental theorem (numerical SDEs)

The curriculum is everything listed on Tentative lecture plan under Topics and Textbooks and notes.
You are supposed to have reasonable control over the the following topics:

• Brownian motion (construction, properties)
• Martingales
• Properties of the Ito integral
• How to solve an SDE by Ito’s formula (examples)
• Linear SDEs
• Some numerical methods for solving SDEs
• Wagner-Platen series (stochastic Taylor expansion)
• Strong and weak convergence
• Linear stability (mean square stability)
• Diffusion processes (Markov processes, generators, transition probabilities/densities)
• Stopping time, the Dynkin’s formula
• Kolmogorovs equations

and from preliminaries:

• Random variables. Expectation value. Conditional expectation.
• The monotone convergence theorem, Fatou’s lemma, the dominated convergence theorem
• Lebesgue integrals (no details required).
• Borel-Cantelli’s lemma