Contents:

• 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.

Detailed Information can be found on the Homepage of 19212901 Basismodul: Stochastics II.

Literature:

• Klenke: Wahrscheinlichkeitstheorie
• Durrett: Probability. Theory and Examples.

Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
Further literature will be given during the lecture.

Prerequisite: Stochastics I  and  Analysis I — III.