# An Introduction to Measure Theoretic Probability

 Lecturer:Class Teacher: Imma Curato Type: MSc Finance course (only) Time and venue: block course 05.10 - 9.1005.10.2015: Lecture: 8:45-12:00 He18, 2.20. 06.10.2015: Lecture: 8:45-10:15  He18, 2.20;   Tutorial: 10:30-12:00  He18, 2.20. 07.10.2015: Lecture: 9:30-12:00 He18, 2.20.  08.10.2015: Lecture: 9:30-12:00 He18, 2.20.  09.10.2015: Exercises: 8:45-10:15 He18, 2.20;  Exercises: 10:30-12:00  He18, 2.20 .22.10.2015: Tutorial: 14:15-15:00 He22, E18; 23.10.2015: Exercises: 12:15-13:45 He18, 2.20from the 12.10  until ChristmasLecture: Monday 10-12 He18, 2.20 Exercises: Wednesday 10-12  He22, Room 202 Tutorial: Wednesday 18:00 - 18:45 He18 E20 (to 02.12.15)LAST Exercise Class: Wednesday, 09.12. 18:00 - 19:30 He18 E20Tutorial: Thursday, 07.01.16 10-12 in H9 Final exam: written exam: 15/01/2016 H11, 15:15-16:45Details:  An Introduction to Measure Theoretic Probability is an open exam.Authorized Auxiliaries:a non-programmable calculator (no smartphone),one A4 sheet or equivalent 2 pages of handwritten notes,a permanent pen. The results are now available in the Hochschulportal.Post exam review: 20.01.2016, 10-12, HeHo 18 Room 2.03. The second written exam will take place  07/04/2016 He220, 10:30-12:00 To register for the second written exam, please write an email to Imma Curato with your name, immatriculation number and course of study. The registrations are open until the 6th April due to technical problems with the HSP. Lecture Notes:  Exercise Sheets: Lecture notes (06.12.2015)  Exercise Sheet 1Exercise Sheet 2 Exercise Sheet 3Exercise Sheet 4Exercise Sheet 5Exercise Sheet 6Exercise Sheet 7Exercise Sheet 8Exercise Sheet 9Solution (Sheet 4 Ex 23 2.) Content: This course covers the basic facts from probability in a measure-theoretic approach.Specific topics aredefinition and properties of measure and Lebesgue integralthe fundamentals of probability: probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theoremthe fundamentals of statistics: simple random sampling, introduction to estimation techniques Literature: H. Bauer, Measure and Integration Theory, De Gruyter Studies in Mathematics, 2011H. Bauer, H., Probability Theory, De Gruyter Studies in Mathematics, 2011P. Billingsley, Probability and Measure, Wiley Series in Probability and StatisticsW. Rudin. Real and Complex Analysis, McGraw-Hill International Editions, 1987J. Jacod & P. Protter, Probability Essentials, 2nd edition, Springer, 2004.E. Kopp, J. Malczak & T. Zastawniak, Probability for Finance, Cambridge University Press, 2014R. Leadbetter, S. Cambanis, V. Pipiras, A Basic Course in Measure and Probability, Cambridge University Press, 2014A. N. Shiryaev, Probability, 2nd edition, Springer, 1995.D. Williams, Probability with Martingales, Cambridge University Press, 1991. Additional Materials Refresher in Probability 1Refresher in Probability 2