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Regular version of the site

Mini-course "Introduction to the theory of Ito SDE"


Professor Alexander Veretennikov (UK, University Leeds)
Leading Research Scientist of the Lab


Plan of mini-course:

1. Winer process: construction and some properties.

2. Stochastic integral and introduction to stochastic differential equations (SDE). Martingales, semimartingales and simplest inequlities for them.

3. Ito's formula about stochastic differential of function. 

4. Ito's theorem about existence and strong uniqueness for SDE.

5. Stochastic exponent, Girsanov Theorem and way of construction of weak SDE's solutions. 

6. Estimation of moments SDE's solutionsa, the dependence of solutions of parameters and initial values, Markov property.

7. The connection of SDE with solution of differential equations of second order.

 

Literature (in Russian):

1. Н.В.Крылов, Введение в теорию случайных процессов, части 1, 2, МГУ, 1986-1987 (lib.mexmat.ru)

2. А.В.Булинский, А.Н.Ширяев, Теория случайных процессов. ФИЗМАТЛИТ, 2005.

3. А.Д.Вентцель. Курс теории случайных процессов. (2-е изд., доп.—М.: Наука. Физматлит, 1996).

Slides in english are available on the following web-site:

4. MAGIC: Stochastic Processes (MAGIC065), 2011/12, http://maths-magic.ac.uk/course.php?id=205

 Working Language: Russian.


Lecture 1




Lecture 2




Lecture 3



Lecture 4




Lecture 5


 

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