Stochastic Differential Equations -- spring semester 2019

QUESTION SESSION before the 2nd exam: Tuesday, the 11th of May 2019, from 10:00, in room H601.

This was the midterm and here are the solutions.
This was the makeup midterm and here are the solutions.
This was the 2nd makeup midterm and here are the solutions.
This was the 1st exam and here are the solutions.
This was the 2nd exam and here are the solutions.

Here is an exam from last year. Questions this year will be similar in flavour.

Results of the semester here.
Explanation of the results:

Course code: BMETE95MM08
Course code for the lecture: T0
Course code for the practice: T1
Official couse data page (in hungarian): TE95MM08
Classes: Lecturer: Tóth Imre Péter. Lectures and practice classes are not strictly separated in schedule.

LECTURE NOTES (hand written by Bálint Tóth, downloadable, these notes cover essentially all material done in class):
1. Brownian motion 1: motivation, phenomenological description, construction
3. Brownian motion 2: construction
2. Brownian motion 3: distributional and path-wise properties
4. Brownian motion 4: quadratic variation
5. Brownian motion 5: reflection principle
6. Filtrations, stopping times, martingales, Markov processes (recap)...
7. Ito calculus 1: the Ito integral
8. Ito calculus 2: Ito’s formula
9. Stochastic differential equations: strong solution, existence and uniqueness
10. Diffusions 1: infinitesimal generator, Dynkin’s formula
11. Diffusions 2: Kolmogorov’s bw and fw equations
12. The Bessel-Squared and the Bessel process NOT DISCUSSED AND NOT NEEDED
13. Diffusions and related elliptic PDEs (Laplace, Poisson, Helmholtz with Dirichlet boundary conditions)
14. Diffusions and related parabolic PDE (Heat eq, Kolmogorov backward and forward eqs, Feynman-Kac formula)
15. Diffusions 3: Feller property, contraction semigroups, Hille-Yosida thm, Feynamn-Kac formula NOT DISCUSSED AND NOT NEEDED
16. Change of measure and Girsanov’s theorem

Problem sheetsHomework assignmentsDue dateSolutions
1. Brownian motion 1.10, 1.12, 1.14, 1.18 28 Feb here
2. Martingales 2.9, 2.10, 2.11 04 April here
3. Ito intergral, Ito formula 3.15, 3.16 08 May here
4. Stochastic differential equations, Dynkin formula, Girsanov theorem 4.3, 4.7, 4.13 on the exam here - except for the hand-in homeworks

REQUIREMENTS There will be regular homework assignments and a written midterm exam during the study period, and a written final exam in the exam period. Homework grading rules: The solution to each homework is evaluated with a "code" with the following meaning: In the end, these codes are translated into scores using the following rule: The final grade, as a function of the total score (on the scale 0-100) is given by the following table:
0-39 scores1
40-54 scores2
55-69 scores3
70-84 scores4
85-100 scores5