# Probability Theory II

WS 2023/24

## Organisation:

Lecture: |
Tuesday, 16:00 - 18:00, M3Thursday, 16:00 - 18:00, M3 |

First lecture: | Tuesday, 10.10.2023 |

Lecturer: | Prof. Chiranjib Mukherjee |

Assistance: | Luzie Kupffer |

Course overview: | This course in the course overview The tutorials in the course overview |

Course syllabus: | We will start by developing the theory of Markov chains further, explore their relations to martingales and give applications to the solution of Dirichlet problem and maximum (resp. comparison) principles. We will then introduce ergodic theory of stationary stochastic processes, and provide applications to central limit theorems for martingales and subsequently, for additive functionals of Markov chains. We will then move on to studying two important types of (continuous time) stochastic processes, namely the Poisson point process and Brownian motion. From this we will finally construct stochastic integrals w.r.t. Brownian motion and cover the rudimentaries of Itô calculus. |

Prerequesites: | As the title of the course suggests, this will be a continuation of the course "Probability Theory" from the Summer semester 2023. Therefore, some knowledge of basic probability theory will be necessary to follow the course. |

Learnweb: | Please enroll in the Learnweb course for this lecture. |

Course assessment: | To be admitted to the exam it is sufficient to earn 50% of the points on the exercise sheets. The type of exam will be announced in the lecture. |