The aim of the course is to introduce basic theories and
methods of pure probability theory at an intermediate level. For example, the student will learn how to compute limits of sequences of stochastic variables by transform techniques. No knowledge of measure and integration theory is required, and only bare first statements of that will be included in the course. Techniques developed in this course are important
in statistical inference, statistical physics, time series analysis, financial analysis, signal processing, statistical mechanics, econometrics, and other branches of engineering and science. The course gives also a
background and tools required for studies of advanced courses in probability and statistics. The course is lectured and examined in English.
Prerequisites:
 SF 1901 or equivalent course a la 'a first course in probability and statistics (for engineers)'
 Basic differential and integral calculus, basic linear algebra.
 Previous knowledge of transform theory (e.g., Fourier transforms) and generating functions
is helpful, but not a necessary piece of prerequisites.
 The concept of Hilbert space will make an appearance, but is not actively required.
Lecturer and Examiner : Boualem Djehiche homepage and contact information
The course web page. http://www.math.kth.se/matstat/gru/sf2940/
Teaching assistants :
 Martina Favero
email
 Philippe Moreillon email
 Lukas Schoug email
 Gustav Zickert
email
 The teaching assistants will each have an office hour open for consultation (1h per week). The hours will be announced later.
Exercise groups
 Martina Favero
 Philippe Moreillon
 Lukas Schoug
 Gustav Zickert
Workshop There will be a 2hour workshop (räknestuga) on a date to be announced later on.
Course literature:
 T. Koski Lecture Notes: Probability and Random Processes Edition 2017 LN pdf
A hardcopy of this text can be bought at THS kårbokhandel (i.e., the bookstore at Campus Valhallavägen), address: Drottning Kristinas väg 19.
 The book by A. Gut An Intermediate Course in Probability, SpringerVerlag 1995 or later editions may be used for a secondary reading reference.
Important: Students, who are admitted to a course and who intend to attend it, need to activate themselves in Rapp . Log in there using your KTHid and click on "activate" (aktivera).
The codename for sf2940 in Rapp is SF2940:sante16.
Examination:
There will be a written examination on Wednesday 24th of October, 2018, 08.00
13.00. Allowed means of assistance for the exam are a calculator (but not the manual for it!) and the Appendix B of Gut, the Collection of Formulas and L. Råde & B. Westergren:
Mathematics Handbook for Science and Engineering.
Each student must bring her/his own calculator, Appendix B of Gut and the Collection of Formulas (that should be downloaded from this homepage) as well as the book by Råde & Westergren to the examination.
The department will NOT distribute the "Formulas and survey".
Grades are set according to the quality of the written examination.
Grades are given in the range AF, where A is the best and F means
failed.
Fx means that you have the right to a complementary examination
(to reach the grade E).
The criteria for Fx is a grade F on the exam, and that an isolated part
of the course can be
identified where you have shown a particular lack of
knowledge and that the examination after a complementary examination on
this
part can be given the grade E.
The Reexam is scheduled to take place on Tuesday December 18, 2018, 08.0013.00.
Preliminary plan Exercises are from the Sections of Problems of LN. For example: Section 1.12.2 1 is the first exercise in section 1.12.2 in LN.
(BD=Boualem Djehiche, MF= Martina Favero, PM= Philippe Moreillon, LS=Lukas Schoug, GZ=Gustav Zickert)
The addresses of the lecture halls and guiding instructions are found at KTH website.
Suggested list of exercises
Solutions to Homework 1 (2017)
Solutions to Homework 2 (2017)
Day 
Date 
Time 
Hall 
Topic 
Lecturer 
Mon 
26/08 
1517 
F2

Lecture 1: Sigmafields, Probability space,
Axioms of probability calculus, Some Theorems of Probability calculus. Distribution functions. Chapter 1 in LN.

BD 
Tue

27/08

0810 
Q31, Q33, Q34, Q36

Exercises 1

MF PM LS GZ

Wed 
28/08

1012 
F1 
Lecture 2: Multivariate random
variables. Marginal density, Independence, Density of a transformed
random vector, Conditional density, Conditional Expectation.
Chapters 23.5 in LN

BD

Fri

30/08 
0810 
Q31, Q33, Q34, Q36

Exercises 2 
MF PM LS GZ

Mon

02/09 
1517 
F2 
Lecture 3: The Rule of Double Expectation E(Y) =
E(E(YX)X), Conditional
variance, The Formula Var(Y) = E (Var(YX)) + Var( E(Y  X)) and its applications, Conditional expectation w.r.t. a sigmafield. Chapter 3 in LN .

BD

Tue

03/09 
0810 
Q31, Q33, Q34, Q36

Exercises 3

MF PM LS GZ

Wed

04/09 
1012 
M1 
Lecture 4: Characteristic fuctions Chapter 4.1.  4.4 LN . 
BD

Fri

06/09 
0810 
Q31, Q31, Q34, Q36

Exercises 4

MF PM LS GZ

Mon

09/09 
1517 
F2 
Lecture 5: More on characteristic functions chapter 4.4 LN Generating functions, Sums of a random number of random variables Chapter 5.2 5.5, 5.7 in LN. 
BD

Tue

10/09 
0810 
Q31, Q33, Q34, Q36

Exercises 5
 MF PM LS GZ

Wed

11/09 
1012 
F1 
Lecture 6: Concepts of convergence in probability 6.26.5 LN

BD

Fri

13/09 
0810 
Q31, Q33, Q34, Q36

Exercises 6 
MF PM LS GZ

Mon
 16/09 
1517 
F2 
Lecture 7: Concepts of convergence in probability theory: convergence by transforms
Convergence of sums and functions of
random variables. Almost sure convergence, strong law of large numbers. Chapter 6.6 6.7 LN

BD

Tue 
17/09 
0810 
Q31, Q33, Q34, Q36

Exercises 7

MF PM LS GZ

Wed

18/09 
1315 
E1 
Lecture 8: Multivariate Gaussian variables, LN Chapter 8

BD

Tue

24/09 
0810 
Q31, Q33, Q34, Q36

Exercises 8

MF PM LS GZ

Wed

25/09 
1012 
F1 
Lecture 9: Gaussian process, covariance properties. Chapter 9.19.4.

BD

Fri

27/09 
1315 
Q34, Q36, V32, V34

Exercises 9 
MF PM LS GZ

Mon

30/09 
1012 
M1 
Lecture 10: Wiener process chapter 10.210.4, Wiener integral 10.5.110.5.2 LN
 BD

Tue

01/10 
0810 
Q31, Q33, Q34, Q36

Exercises 10 
MF PM LS GZ

Wed

02/10 
1012 
F1 
Lecture 11: Ornstein Uhlenbeck process, chapter 11.2 LN

BD

Tue 
08/10 
0810 
Q31, Q33, Q34, Q36

Exercises 11

MF PM LS GZ

Wed

09/10 
0810 
F1 
Lecture 12: Reserve, repetition, summary 
BD

Thu

10/10 
0810 
Q31, Q33, Q34, Q36

Exercises 12: Repetition and old exams

MF PM LS GZ

some day in Week 42

To be announced 
To be announced 
To be announced later on

Workshop (Räknestuga) in Probability Theory

MF PM LS GZ

Wed

23/10 
0813 
See the relevant web page for further information or
this web page 
Exam

BD

Welcome, we hope you will enjoy the course (and learn a lot)!
Boualem, Martina, Gustav, Lukas and Phillippe.
To course
web page
