Lehre
Dozent:in: David Criens
Assistenz: Samuel Adeosun
Sprache: auf Englisch
Inhalt
This lecture builds the foundation of one of the key areas of probability theory: stochastic analysis. We start with a rigorous construction of the It^o integral that integrates against a Brownian motion (or, more generally, a continuous local martingale). In this connection, we learn about It^o's celebrated formula, Girsanov’s theorem, representation theorems for continuous local martingales and about the exciting theory of local times. Then, we discuss the relation of Brownian motion and Dirichlet problems. In the final part of the lecture, we study stochastic differential equations, which provide a rich class of stochastic models that are of interest in many areas of applied probability theory, such as mathematical finance, physics or biology. We discuss the main existence and uniqueness results, the connection to the martingale problem of Stroock-Varadhan and the important Yamada-Watanabe theory.
Vorkenntnisse
Wahrscheinlichkeitstheorie I und II (Stochastische Prozesse)
Verwendbarkeit
Advanced Lecture in Stochastics
Elective in Data