MAT4700 - V?r 2007

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
16.01.2007Giulia diNunno? B62 NHA'shus? Introduction? Introduction to the course. Preliminaries from probability, measure theory and analysis.?
17.01.2007? ? ? Preliminaries from probability, measure theory and analysis.

Here you find a summary of all the arguments touched in class and references.

Here is a list of suggested exercises.?

23.01.2007? ? Stochastic processes and Brownian motion? Stochastic processes, Kolmogorov extension theorem, Kolmogorov continuity theorem, Brownian motion. Details are here

Suggested exercises are here?

25.01.2007? ? ? No classes?
30.01.2007? ? Revision? Exercise session?
01.02.2007? ? Brownian motion and the regularity of its trajectories. Introduction to stochastic integration? Study of the p-variation of Brownian motion, Levy theorem, the consequences into the construction of a stochastic integral. Details are here?
06.02.2007? ? Ito stochastic intregration? Constraction of the Ito stochastic integration (i.e. non-anticipating integration or integration adapted to the flow of information)?
08.02.2007? ? ? Properties of the Ito stochastic integral and the process of integrals. Generalizations of the Ito integration. Details can be found here

Suggested exercises are here?

13.02.2007? ? Revision? Exercise session?
15.02.2007? ? Ito formula: the chain rule? Motivations and main theorem with proof.

Suggested exercises: [?] 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.10, 4.11.?

20.02.2007? ? Revision? Exercise session?
22.02.2007? ? Ito representation theorem and stochastic differentiation? Motivations, Ito representation theorem, martingale representation theorem. Non-anticipating stochastic derivative ( notes )

Details can be found here

Suggested exercises: [?] 4.12, 4.13, 4.14, 4.15?

27.02.2007? ? Revision and Introduction to SDE? First and exercise session. Then we have introduced SDE, the basic related questions, the meaning of strong and week solution, the meaning of strong and week uniqueness. The geometric Brownian motion?
01.03.2007? ? SDE? Existence and uniqueness of the solution of an SDE. Theorm with proof.

Suggested exercises: [?] 5.1, 5.6?

06.03.2007? ? SDE? Continuity of the solution of an SDE. Strong and Weak solution, the Tanaka equation. Short exercise session to finish.

Details can be found here

Suggested exercises: [?] 5.3, 5.4, 5.5, 5.7, 5.11, 5.12?

08.03.2007? ? SDE conclusion and revision? Exercise session and solution of a general linear SDE?
13.03.2007? ? Ito diffusions? Markov property. Strong Markov property?
15.03.2007? ? Ito diffusions? Infinitesimal generator of a diffusion

Suggested exercises: [?] 7.1, 7.2, 7.3, 7.4, 7.8, 7.15, 7.18. Take a look at 7.12. In addition you have also these?

20.03.2007? ? Ito diffusions? Characteristic operators. Applications. Conclusion of the program.

Details on last part of the program are here?

22.03.2007? ? Conclusion of the program? This is the last lecture in this course. It is an exercise session. We will also revise the "pensum" for the exam.

For those who are interested, the follow up of this course is "Stochastic Analysis II", MAT4711. Please visit the corresponding web-page.?

Publisert 11. jan. 2007 21:43 - Sist endret 15. mars 2007 20:00
Del p? e-post