Statistics for stochastic processes (2018-2019).
The goal of these lectures is to give an elementary introduction to statistical inference for stochastic processes in discrete and continuous time. The course will, essentially, be divided in two parts: statistics for time series and statistics for diffusion processes. In the first part, the focus will be on stationary processes (autoregressive processes, moving average processes, ARMA processes) and spectral theory. In the second part, the emphasis will be on stochastic processes in continuous time and especially on nonparametric estimation of the drift and the diffusion coefficient of a diffusion process.
The course requires basic knowledge in probability theory, real and complex analysis, basic facts about L_p spaces and Brownian motion. Also, some knowledge of stochastic calculus would be helpful, but it is not necessary. The course is addressed to Master level students and it has been structured having in mind a mixed audience of students from different departments (Mathematics, Statistics, Computer Science, Physics, Economics, etc.). The material will be therefore presented in a rigorous but simple way with a special emphasis on the motivation of concepts and applications.
The lectures are every Tuesday from 10h15 to 11h45 and Thursday from 08h15 to 09h45, Raum 2.09.0.14 (Golm). The exercises are every Thursday from 10h15 to 11h45, Raum 2.09. 0.13 (Golm).
Statistics for stochastic processes (2017-2018).
- Lecture 1: Lecture notes, Exercises
- Lecture 2: Lecture notes, Exercises
- Lecture 3: Lecture notes
- Lecture 4: Lecture notes, Exercises
- Lecture 5: Lecture notes
- Lecture 6: Lecture notes, Exercises
- Lecture 7: Lecture notes
- Lecture 8: Lecture notes, Exercises
- Lecture 9: Lecture notes
- Lecture 10: Lecture notes
Exercitations (travaux dirigés) in M231a - Matrix calculus. (2013-2014).
Exercitations (travaux dirigés) in M231b - Calculus. (2013-2014).
Exercitations (travaux dirigés) in MAT239 - Algebraic Structures. (2012-2013).
Oral tests (colles) in MAT242 - Function series and Fourier series. (2012-2013).
Oral tests (colles) in MAT241 - Bilinear algebra and applications. (2012-2013).