19212901 Basismodul: Stochastics II
Summer Term 2020
Time and place
Lecture: Video lectures will be available online (see below).
Online "office hours": Tuesdays 12:30-14:00. The link to the Webex session can be found in the Whiteboard system.
- Exercise Session: Tuesdays, 16:00-17:30, online. The link to the Webex session can be found in the Whiteboard system.
- Final Exam: to be announced in due course
Prerequisits: Stochastics I und Analysis I — III.
To receive credits fo the course you need to
- actively participate in the exercise session
- work on and successfully solve the weekly exercises
- pass the final exam (see above)
If you are an FU student you only need to register for the course via CM (Campus Management).
If you are not an FU student, you are required to register via KVV/Whiteboard.
Problem sets will be put online every Tuesday and can be found under Assignements in the KVV/Whiteboard portal. Solutions (in groups of three!) are due by 4pm on Tuesday of the following week – solutions must be uploaded through the KVV/Whiteboard portal or sent by email to Helena Kremp.
Course Overview/ Content:
- Construction of stochastic processes;
- conditional expectation;
- martingales in discrete time: convergence, stopping theorems, inequalities;
- convergence types in stochastics;
- uniform integrability;
- Markov chains in discrete and continuous time: recurrence and transience, invariant measures;
- convergence in distribution of stochatic processes;
- Brownian motion and invariance principle.
- Klenke: Wahrscheinlichkeitstheorie
- Durrett: Probability. Theory and Examples.
Further literature will be given during the lecture.
- Videos for Tuesday, April 21:
- Introduction (Section 0 of the notes)
- Definition of stochastic process (1.1-1.2)
- Distribution of a stochastic process (1.3-1.5)
- Finite-dimensional distributions of a stochastic process (1.6-1.7)
- Videos for Thursday, April 23:
- Videos for Tuesday, April 28:
- Videos for Thursday, April 30:
- Construction of product measures & Gaussian processes (1.19-1.20)
- First example of a Markov chain (1.21)
- Definition of a Markov chain (1.22-1.26)
- Construction of Markov chains (1.27-1.28)
- Videos for Tuesday, May 5:
- Videos for Thursday, May 7:
- (Short) Videos for Tuesday, May 12:
- Videos for Thursday, May 14:
- Videos for Tuesday, May 19:
- Videos for Tuesday, May 26: