MAIN REFERENCE Zdzisław Brzeźniak, Tomasz Zastawniak, Basic Stochastic Processes: A Course Through Exercises, Springer 1999. 

link: https://eclass.uoa.gr/modules/document/file.php/MATH437/%CE%92%CE%BF%CE%B7%CE%B8%CE%B7%CF%84%CE%B9%CE%BA%CF%8C%20%CF%85%CE%BB%CE%B9%CE%BA%CF%8C/Biblio1.pdf

A good reference in Greek

http://users.uoa.gr/~dcheliotis/SimeioseisStocCalc.pdf

Interesting and possibly helpful senior thesis in Greek

https://ir.lib.uth.gr/xmlui/bitstream/handle/11615/52080/20209.pdf?sequence=1

CLASSES TAKE PLACE TUESDAY AND THURSDAY AT 3.15-5, ROOM A212.

Ασκήσεις θα γίνονται και στα Ελληνικά, Τετάρτες 1-3, στην Ε204.

FINAL EXAM: MAY 29, 9-11.  A sheet (A4) of handwritten notes is allowed. 

OFFICE HOURS Tuesday 2-3, Δ338

CALENDAR

13/2 3-6pm: σ-fields, Probability function, Borel sets, Lebesgue measure, Borel-Cantelli lemma, Random variables (section 1.1  from BZ)

15/2 3-6pm: Random variables, Probability distribution functions, Density functions (section 1.2  from BZ)

20/2 3-6pm: Expected values, Conditional Probability, Independence  (sections 1.2, 1.3  from BZ). Conditional Expectation. Conditioning on an event (section 2.1 from BZ)

22/2 3-6pm: Conditional Expectation. Conditioning on a discrete random variable  (section 2.2 from BZ) 

27/2 3-5pm: Conditional Expectation. Conditioning on an arbitrary random variable  (section 2.3 from BZ) 

29/2 3-5pm: Conditional Expectation. Conditioning on an arbitrary random variable: examples and exercises  (section 2.3 from BZ) 

5/3   3-5pm: Conditional Expectation. Conditioning on an arbitrary random variable: examples and exercises  (section 2.3 from BZ) 

12/3  3-5pm: Conditional Expectation. Conditioning on a σ-field (section 2.4 from BZ). General Properties (section 2.5 from BZ)

19/3  3-6pm: Conditioning on a σ-field. General Properties (section 2.5 from BZ). Exercises (section 2.6 from BZ)

21/3 3-6pm. Martingales (sections 3.1-3.3 from BZ)

26/3 3-5pm. Midterm

28/3 3-6pm. Games of Chance. Stopping Times (sections 3.4-3.5 from BZ)

2/4 3-6pm.  Continuous time. Poisson process (sections 6.1-6.2 from BZ)

4/4 3-5pm.  Brownian motion (section 6.3 from BZ)

9/4 3-5pm. Increments of Brownian Motion  (section 6.3 from BZ)

11/4 3-5pm. Sample paths (section 6.3 from BZ)

16/4 3-5pm. Two exercises (section 6.3 from BZ).  Ito integral. Random step processes  (section 7.1 from BZ)

18/4 3-5pm.  Ito integral: general case (section 7.1 from BZ)

23/4 3-5pm.  Ito integral: martingale (section 7.1 from BZ)

25/4 3-5pm.  Ito integral: continuous paths (section 7.1 from BZ).  Examples (section 7.2 from BZ)

14/5 3-5pm.  Ito integral: basic properties (section 7.3 from BZ)

15/5 9-11am.  Stochastic Differential and Ito formula (section 7.4 from BZ)

ΒΑΘΜΟΙ ΠΡΟΟΔΟΥ -  MIDTERM GRADES

AM                                       grade

2981                                         9,5

6156                                         3,5

6034                                            0

2620                                          4,5

3030                                          2,5

2532                                          7

5273                                          3

3062                                          1

5866                                          4

2515                                          5   

2901                                           7,5

2968                                           8

6535                                           10

2950                                            8,5

5972                                             5

6213                                           2,5

2886                                            7,5   

6283                                            7,5

2612                                              1

2684                                              1,5

6054                                              1,5

2676                                                0                  

5014                                                 8

6230                                                4,5

6040                                                5

5910                                                 2

2888                                                0

2693                                                 0

1874                                                 6,5

2804                                                  0

1794                                                  5,5

2662                                                   6