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.
  
• Boris Petkovic email.
  
• Lukas Schoug email Office hours: Wednesdays at 15.30-16.30, Room 3732.
  
• Philippe Moreillon 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
  
• Boris Petkovi
  
• Lukas Schoug
  
• Philippe Moreillon

Workshop There will be a 2-hour workshop (räknestuga) on a date to be announced later on.

Course literature:

• T. Koski Lecture Notes: Probability and Random Processes Edition 2017 LN pdf

• The book by A. Gut An Intermediate Course in Probability, Springer-Verlag 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 KTH-id 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 A-F, 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 Re-exam is scheduled to take place on Tuesday December 18, 2018, 08.00-13.00.
  
  
  

  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, BP=Boris Petkovic, LS=Lukas Schoug, PM= Philippe Moreillon ) 
  The addresses of the lecture halls and guiding instructions are found at KTH website.
  
  Suggested list of exercises
  
  Solutions to some exercises Session 1
  
  Solutions to some exercises Session 2
  
  Solutions to some exercises Session 3
  
  Solutions to some exercises Session 4
  
  Solutions to some exercises Session 5,6
  
  Solutions to some exercises Session 7
  
  Solutions to some exercises Session 8
  
  Solutions to Homework 1 (2017)
  
  Solutions to Homework 2 (2017)
  
  Last session
  
  Problems from old exams

  
  
  

  Day	Date	Time	Hall	Topic	Lecturer
  Tue	28/08	15-17	F1	Lecture 1: Sigma-fields, Probability space, Axioms of probability calculus, Some Theorems of Probability calculus. Distribution functions. Chapter 1 in LN.	BD
  Wed	29/08	13-15	Q31, Q33, Q34, Q36	Exercises 1	MF LS PM BP
  Fri	31/08	10-12	F2	Lecture 2: Multivariate random variables. Marginal density, Independence, Density of a transformed random vector, Conditional density, Conditional Expectation. Chapters 2-3.5 in LN	BD
  Fri	31/08	15-17	Q31, Q33, Q34, Q36	Exercises 2	MF LS PM BP
  Mon	03/09	08-10	F1	Lecture 3: The Rule of Double Expectation E(Y) = E(E(Y|X)|X), Conditional variance, The Formula Var(Y) = E (Var(Y|X)) + Var( E(Y | X)) and its applications, Conditional expectation w.r.t. a sigma-field. Chapter 3 in LN .	BD
  Tue	04/09	15-17	Q31, Q33, Q34, Q36	Exercises 3	MF LS PM BP
  Wed	05/09	13-15	F1	Lecture 4: Characteristic fuctions Chapter 4.1. - 4.4 LN .	BD
  Fri	07/09	10-12	Q34, Q36, V22, V32	Exercises 4	MF LS PM BP
  Mon	10/09	08-10	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	11/09	15-17	Q31, Q33, Q34, Q36	Exercises 5	MF LS PM BP
  Wed	12/09	13-15	FR4 (Albanova)	Lecture 6: Concepts of convergence in probability 6.2-6.5 LN	BD
  Fri	14/09	10-12	Q34, Q36, V22, V32	Exercises 6	MF LS PM BP
  Mon	17/09	08-10	FR4 (Albanova)	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	18/09	15-17	Q31, Q33, Q34, Q36	Exercises 7	MF LS PM BP
  Fri	21/09	10-12	F1	Lecture 8: Multivariate Gaussian variables, LN Chapter 8	BD
  Mon	24/09	08-10	Q31, Q33, Q34, Q36	Exercises 8	MF LS PM BP
  Tue	25/09	15-17	F1	Lecture 9: Gaussian process, covariance properties. Chapter 9.1-9.4.	BD
  Wed	26/09	13-15	Q31, Q33, Q34, Q36	Exercises 9	MF LS PM BP
  Mon	01/10	08-10	F1	Lecture 10: Wiener process chapter 10.2-10.4, Wiener integral 10.5.1-10.5.2 LN	BD
  Tue	02/10	15-17	Q31, Q33, Q34, Q36	Exercises 10	MF LS PM BP
  Wed	03/10	13-15	FR4 (Albanova)	Lecture 11: Ornstein Uhlenbeck process, chapter 11.2 LN	BD
  Mon	08/10	08-10	Q31, Q33, Q34, Q36	Exercises 11	MF LS PM BP
  Tue	09/10	15-17	F2	Lecture 12: Reserve, repetition, summary	BD
  Wed	10/10	13-15	Q31, Q33, Q34, Q36	Exercises 12: Repetition and old exams	MF LS PM BP
  some day in Week 42	To be announced	To be announced	To be announced later on	Workshop (Räknestuga) in Probability Theory	MF LS PM
  Wed	24/10	08-13	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, Boris, Lukas and Phillippe

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  To course web page