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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Stochastic Analysis SemesterSoSe 2026 Lecturer Richard Höfer Type of course (Veranstaltungsart) Vorlesung German title Stochastische Analysis Contents We develop the theory of stochastic integration and stochastic differential equations, which play a fundamental role in many aspects of natural sciences, computer science and finance. After a systematic study of continuous time martingales we introduce Itô calculus to integrate against a stochastic processes such as Brownian Motion. Since Brownian Motion has unbounded total variation, this requires a generalization of the Lebesgue integral and the Stieltjes integral. We will cover the Itô Formula, quadratic variation, Levy's characterization of Brownian Motion, Stratonovitch integrals, Girsanov transform, Black Scholes formula, Feynman-Kac formula and stochastic representation of solutions to PDEs. Literature Klenke: Wahrscheinlichkeitstheorie. Le Gall: Brownian Motion, Martingales, and Stochastic Calculus. Rogers and Williamns: Diffusion, Markov Processes, and Martingales. Kuo: Introduction to Stochastic Integration. Protter: Stochastic Integration and Differential Equations. Recommended previous knowledge Lineare Algebra, Analysis, Introduction to probability theory. Knowledge in Functionalanalysis, partial differential equations or optimization is helpful but not required Time/Date Tue 10-12, Thu 12-14; Exercise: Mon 14-16 Location Tue: M 102, Thu: M 104; Exercise M102 Course homepage https://elearning.uni-regensburg.de/course/view.php?id=980717 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MAngAn ECTS 9 |