Stochastische Analysis
General
| Lecture: |
Tuesday , 12-2 pm, M2 |
| start of lectures: |
Tuesday, October 8, 2024 |
| Lecturer: | Prof. Chiranjib Mukherjee |
| Tutorials: | Mittwoch, 10-12 am, SR4 |
| Assistance: | Pavlos Zoubouloglou |
| KommVV: | Eintrag der Vorlesung im kommentierten Vorlesungsverzeichnis Eintrag der Übungen im kommentierten Vorlesungsverzeichnis |
| Contents: |
Stochastic analysis is a fundamental topic in probability theory that is linked to various areas of mathematics (e.g. partial differential equations, mathematical physics, geometry) and has applications in finance, chemistry and biology. The target audience of the Stochastic Analysis course are mathematics students who are already familiar with the basic concepts of probability theory. As for the content, we will first present various constructions of Brownian motion and discuss some of its basic probabilistic, analytical and statistical properties, such as the Markov property. Then, we will define stochastic integrals in the Itô sense in terms of general continuous local martingales such as Brownian motion. We will also discuss the properties of such integrals, such as the Itô formula. Then, we will present three concrete applications of this theory, namely, we will a) construct “local times” of Brownian motion, b) investigate stochastic (ordinary) differential equations, i.e. evolution equations driven by random noise, and c) Analyze martingale problems and general continuous-time Markov processes. |
| Some basic knowledge of probability theory will be necessary to follow this lecture. The course will be held in English. | |
| Learnweb: |
Please enroll in the Learnweb course for this lecture. |
| Leistungsnachweis: |
To be admitted to the exam, it is sufficient to achieve 50% of the points on the exercise sheets. The type of exam will be announced in the lecture. |