MAT4700 - V?r 2005

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
18.01.2005Giulia di Nunno? Auditorium 3 Vilhelm Bjerknes hus? Welcome to the course! ? A presentation of the course is available here

Preliminaries: probability spaces.

Ref. [O] Ch. 1, 2.?

19.01.2005GdN? Math. Building B62? Preliminaries: random variables, distributions.? Ref. [O] Ch. 2

Further references:

  • P. Billingsly, "Probability and measure", Wiley 1995
  • J. Jacod and P. Protter, "Probability essentials", Springer 2000.

Might be of your interest:

  • A.N. Kolmogorov, "Foundations of the theory of probability", Chelsea Publishing company 1956.
  • A.N. Kolmogorov and S.V. Fomin, "Elements of the theory of functions and functional analysis", Graylock Press 1961.
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20.01.2005GdN? Math. Building B62 ? Preliminaries: distributions, independence. Conditional expectation.? The detailed description of the material discussed and required on "Preliminaries on Measure Theory and Probability theory" is here

Suggested exercises are here?

25.01.2005GdN? Math. Building B63? Exercise session.? Correction and discussion in class on selected exercises.?
26.01.2005GdN? Math. Building B62 ? Introduction to stochastic processes: general theory.? A detailed description of the material discussed and further references is here?
27.01.2005GdN? Math. Building B62 ? Introduction to stochastic processes: Brownian motion? A detailed description of the material discussed and further references is here

Suggested exercises are here?

01.02.2005GdN? Math. Building B63 ? Exercise session.? Correction and discussion in class on selected exercises. ?
08.02.2005GdN? Math. Building B63 ? Ito Integrals. Motivation and construction.? A detailed description of the material discussed and further references is here?
09.02.2005GdN? Math. Building B63? Properties of the Ito integrals.? A detailed description of the material discussed and further references is here?
10.02.2005GdN? Math. Building B63? Properties of the Ito integrals and extensions.? A detailed description of the material discussed and further references is here

Suggested exercises are here?

15.02.2005GdN? Math. Building B63? Exercise session.? Correction and discussion in class on selected exercises. ?
16.02.2005GdN? Math. Building B63? Ito formula.? A detailed description of the material discussed and further references is here

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

17.02.2005GdN? Math. Building B63? Ito representation theorem.? A detailed description of the material discussed and further references is here

Suggested exercises are: [?] 4.14, 4.15, 4.16?

22.02.2005GdN? Math. Building B63? Elements of stochastic differentiation. Exercise session.? A detailed description of the material discussed and further references is here

The material on stochastic differentiation can be found in this notes?

23.02.2005GdN? Math. Building B63? Stochastic differential equations? A detailed description of the material discussed and further references is here??
24.02.2005GdN? Math. Building B63? Stochastic differential equations? A detailed description of the material discussed and further references is here

Suggested exercises are: [?] 5.1, 5.3, 5.4, 5.5, 5.6, 5.7, 5.11, 5.12?

02.03.2005Inga B. Eide? Math. Building B63. N.B. Time 14.15-17.00 (circa)? Exercise session.? Correction in class on selected exercises. ?
08.03.2005GdN? Math. Building B63? Ito diffusions: definition and Marckov property? A detailed description of the material discussed and further references is here?
09.03.2005GdN? Math. Building B63? Ito diffusions: strong and generalized Markov properties. The generator.? A detailed description of the material discussed and further references is here?
10.03.2005GdN? Math. Building B63? Ito diffusions: The Dynkin formula. The characteristic operator.? A detailed description of the material discussed and further references is here

Suggested exercises are: [?] 7.1, 7.2, 7.3, 7.4, 7.8(a), 7.10, 7.15, 7.18.?

17.03.2005GdN? Math. Building B63? Exercise session? Correction in class on selected exercises. ?
01.04.2005? ? ? FINAL EXAM 4700

MID-TERM EXAM 4710

It is an oral examination. Theoretical questions and the solution of an exercise will be asked.

Sensor: Prof. Jan Ub?e (NHH, Bergen)?

06.04.2005? ? ? The course MAT4700 is closed. The details about the program in MAT4710 can be found at this page?
Publisert 8. des. 2004 11:43 - Sist endret 29. mars 2005 12:09
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