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Stochastic analysis I, spring 2017
Teaching schedule (old).
Weeks 3-9, Tuesday 12-14 and Thursday 10-12 in room B120. Exercise class on Wednesdays 10-12 in B120. The first lecture is on tuesday 17.1,
The course continues in the IV teaching period as Stochastic analysis II, with the new teaching schedule:
Weeks 11-18, lectures on Wednesday 12-14 in B120 and Thursday 12-14 in room D123, and exercises on Tuesday 10-12 in room D123
Easter holiday 13.-19.4.
Exam lasts 2,5 hours.
You can use (lecturer will fill in) in the exam.
lecture notes (last update on 10.5.2017)
levybm.m octave function showing Paul Levy construction of Brownian motion.
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.
Daniel Revuz and Marc Yor, Continuous martingales and Brownian motion, 2nd edition Springer 2005.
week 1: We have discussed Kolmogorov extension theorem for a family of consistent finite dimensional probability distributions (without proof), proved Paul Levy theorem about the construction of Brownian motion, introducing also the Cameron Martin space.
week 2,3: We have proved Kolmogorov continuity theorem, almost sure non-differentiability and Hölder-continuity of Brownian paths. We have also proved Doob backward martingale convergence theorem (in discrete time), and shown that Brownian motion has quadratic variation [ B ]t = t , where the convergence is in L2 and also almost surely when the sequence of discretizing partitions is refining (see Prop 7,8 in the lecture notes).
Did you forget to register? What to do?
- exercise 1 (27.1 and 1.2 2017)
- exercise 2 (8.2)
- exercise 3 (22.2)
Solve exercises 3.8, 3.13, 3.15, 3.16, 3.17, 3.18, 3.19, 16.1,16.2, 16.3 from R.Bass book Stochastic Processes.
exercise 4 (14.3 and 21.3)
Course feedback can be given at any point during the course. Click here.