Richard Bass, Stochastic processes, Cambridge University Press 2011.
Fabrice Baudoin, Diffusion Processes and Stochastic Calculus. European Mathematical Society Ems Textbooks in Mathematics 2014.
Alexander Gushchin, Stochastic calculus for quantitative finance. ISTE Press, Optimization in insurance and finance 2015.
René L Schilling Lothar Partzsch, Brownian motion, an introduction to stochastic processes, De Gruyter 2012.
Sheng-wu He, Jia-gang Wang, Jia-an Yan, Semimartingale Theory and Stochastic Calculus, CRC 1992.
Jean Jacod and Albert Shiryaev, Limit theorems for stochastic processes, 2nd edition Springer 2003.
Hui-Hsiung Kuo, Introduction to stochastic analysis, Springer 2006.
Jean-François Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer 2016.
Mörters and Peres, Brownian motion, Cambridge 2010.
Ashkan Nikeghbali, An essay on the general theory of stochastic processes, Probability Surveys Vol. 3 (2006) 345-412.
Daniel Revuz and Marc Yor, Continuous martingales and Brownian motion, 2nd edition Springer 2005.
Home exam, to be returned by June 4 2018.
The course is passed by solving the weekly assignments and by writing an home exam.
Master's Programme in Mathematics and Statistics is responsible for the course.
The course belongs to the Mathematics and Applied mathematics module.
Probability theory I,II, and their prerequisites
Stochastic calculus for semimartingales
Recommended time/stage of studies for completion: 1. or 2. year
Term/teaching period when the course will be offered: varying
The course is focused on stochastic integration theory, with respect to martingales and processes with finite variations, including continuous martingales and processes with jumps.
Lecture notes, Bass "Stochastic Processes" CUP
Exam, other methods will be described later