MAT4700 - Spring 2008

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
14.01.2008Giulia diNunno? B70 NHA's Hus? Introduction? WELCOME TO "STOCHASTIC ANALYSIS"

Preliminaries from probability, measure theory and analysis.

Here you find a summary of the topics that will be touched in class and some extra references for those interested.?

15.01.2008GdN? B62 NHA's Hus? ? Continuation of Introduction

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16.01.2008GdN? B71 NHA's Hus? Stochastic processes and Brownian motion? Stochastic processes, Kolmogorov extension theorem, Kolmogorov continuity theorem, Brownian motion. Details are here

Material for the forthcoming exercise sessions can be found here and here?

22.01.2008? ? ? No classes?
23.01.2008An Ta Thi Kieu? B71 NHA's Hus? Exercise session? ?
25.01.2008ATTK? B71 NHA's Hus? Exercise session? ?
29.01.2008GdN? B70 NHA's Hus? Brownian motion? Construction of Brownian motion via Kolmogorov theorems, regularity of the paths (continuity, no differentiability, quadratic variation and Levy theorem), martingales.?
30.01.2008GdN? B71 NHA's Hus ? Stochastic integration? Revision of Riemann-Stieltjes integration and its potential applicability to Brownian motion as integrator: discussion?
01.02.2008GdN? B71 NHA's Hus ? Ito stochastic integration (non-anticipating integration)? Construction of the Ito integral.

Detailed list of topic covered this week can be found here

New material for the forthcoming exercise sessions can be found here?

05.02.2008GdN? B70 NHA's Hus? Ito stochastic integration and properties? Properties of the integral and of the process of integrals on time.?
06.02.2008ATTK? B71 NHA's Hus ? Exercise session? ?
08.02.2008ATTK? B71 NHA's Hus ? Exercise session? ?
12.02.2008GdN ? B70 NHA's Hus ? Extension of the Ito integral and Ito formula? Extensions of the construction of the Ito integral within the non-anticipating setting. Introduction to the possible extension of the Ito integral to other anticipating settings. About the Ito formula in dimension 1.

Suggested exercises: [?] 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 7.12, 7.8 (a,b).

In addition you can also try these?

13.02.2008GdN ? B71 NHA's Hus? More on Ito formula? Conclusion of the proof. Ito formula in multi-dimension. Integration by parts formula.?
15.02.2008ATTK ? B71 NHA's Hus? Exercise session? ?
19.02.2008GdN ? B70 NHA's Hus? Ito representation theorem and martingale representation theorem? Discussion of the topic and the two theorems in detail.?
20.02.2008GdN? B71 NHA's Hus ? Stochastic non-anticipating differentiation. Introduction to stochastic differential equation.? A summary of the topics treated these days is here

Notes about the non-anticipating stochastic derivative are here?

22.02.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus? Exercise session? ?
26.02.2008GdN? B1036 NHA's Hus? Stochastic differential equations (SDEs)? Existence and uniqueness of the (strong) solution of an SDE.

Suggested exercises: [?] 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12 and this one ?

27.02.2008GdN? B1036 NHA's Hus? Stochastic differential equations (SDEs) ? Weak solution, weak uniqueness, Tanaka equation.?
29.02.2008GdN? Auditorium 3 Vilhelm Bjerknes hus? Ito diffusions - Markov property? Some comments on the property of SDEs. Case study, geometric Brownian motion. Ito diffusion, homogenuity, Markov property.

A summary of the topics treated about SDEs here

Some more exercises to try out: [?] 5.13, 5.14, 5.15, 5.16, 5.18?

04.03.2008GdN? B1036 NHA's Hus? Ito diffusions - strong Markov property? More about Markov properties and Ito diffusions, stronger and stronger versions?
05.03.2008GdN? B1036 NHA's Hus? Generator of a diffusion and Dynkin formula? We have concluded the chapter proving the relationship between the generator of a diffusion and a second order differential operator and we have concluded presenting the Dynkin formula.

A summary of the topics treated about Ito diffusions is here

Suggested exercises: [?] Example 7.4.2, Exercises 7.1, 7.2, 7.3, 7.4, 7.8, 7.9, 7.10, 7.15, 7.18, 7.20.

This is last class of lectures in the course MAT4700. The exams will be held April 21st, 22nd 23rd.?

07.03.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus? Exercise session? ?
12.03.2008ATTK? B1036 NHA's Hus? Exercise session? ?
14.03.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus? Exercise session? ?
26.03.2008? ? ? ??
28.03.2008? ? ? ??
Published Jan. 3, 2008 1:10 PM - Last modified Mar. 5, 2008 6:33 PM
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