Dozentin: Olga Aryasova
- Termin und Ort: Montag, 16-18 Uhr, in SE 30.00.001; Dienstag 12-14 Uhr in 00.103 (BSZ)
- Übungen (Vst.-Nr. 08045060): Dienstag 16-18 Uhr in SE 40.00.001, ab 24.10.2023
- Beginn: 16.10.2023
- Sprache: Englisch
The exploration and understanding of real-world phenomena, ranging from natural catastrophes to stock price evolutions, have led to the development of the concept of stochastic processes. To study the behavior of the random processes, a comprehensive framework called stochastic calculus was created.
In this course, we will start with the fundamental definitions and examples of stochastic processes. Then we will introduce a Wiener process, which plays a vital role in stochastic calculus, diffusion processes and even potential theory. We will delve into stochastic integration and stochastic differential equations, crucial tools for analyzing and modeling the behavior of stochastic processes. In the last part of the course, we will uncover the connection between stochastic processes and potential theory and show how a Wiener process can be utilized to solve classical boundary problems for parabolic partial differential equations. The course will also cover some simulation techniques for stochastic processes.
Voraussetzungen: Grundkenntnisse der Stochastik
H.-H. Kuo, Introduction to Stochastic Integration, Springer, 2006
I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Springer, second edition, 1991
R. L. Schilling, L. Partzsch, Brownian Motion, De Gruyter, 2012
R. Durrett, Stochastic Calculus: A Practical Introduction (1st ed.), 1996