This course covers the basic but nevertheless relevant (especially for Financial Mathematics I) topics of probability theory in a measure-theoretic approach.

Specific topics are

• Definition and properties of measure and the Lebesgue integral.
• The fundamentals of probability: probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theorem.
• An introduction to statistics: simple random sampling, introduction to estimation techniques.

More information is given in Moodle. Please inscribe there to the course.

Available in the library.

• H. Bauer, Measure and Integration Theory, De Gruyter Studies in Mathematics, 2011.
• H. Bauer, Probability Theory, De Gruyter Studies in Mathematics, 2011.
• P. Billingsley, Probability and Measure, Wiley, 2012.
• D. L. Cohen, Measure Theory, Birkenhäuser, 2010.
• J. Jacod & P. Protter, Probability Essentials, 2nd edition, Springer, 2004.
• A. Klenke, Probability Theory - A Comprehensive Course, Springer, 2006.
• E. Kopp, J. Malczak & T. Zastawniak, Probability for Finance, Cambridge University Press, 2014.
• R. Leadbetter, S. Cambanis, V. Pipiras, A Basic Course in Measure and Probability, Cambridge University Press, 2014.
• A. N. Shiryaev, Probability, 2nd edition, Springer, 1995.
• W. Rudin, Real and Complex Analysis, McGraw-Hill International Editions, 1987.
• D. Williams, Probability with Martingales, Cambridge University Press, 1991.