Oberseminar AG Mathematische Modellierung

Montag, den 08. Juli 2024 um 17.00 Uhr in B7- 210 - Seminarraum A

Vortrag von Richard Boadi (Clausthal) zum Thema "Understanding the principles of SDEs".


In this talk, I will try to explain the basic principles needed to understand SDEs. I present preliminaries of Stochastic processes and one example I looked at is the Brownian motion and its properties with graphical representation. I further explain filtrations and the types, adapted processes and the types and quadratic variations with examples. Moreover, I look at stochastic integration where I introduce an abbreviation of the stochastic integral in the continuous form and then move on to explain elementary processes, stochastic integral in the discrete form, the elementary properties of stochastic integrals, approximation by the elementary processes, Ito integral and the Ito lemma with a short sketch of the proof for both Ito integral and lemma. I conclude with SDEs by introducing an abbreviation of an SDE with a solution to it. I explain the types of solutions (i.e. strong and weak) with emphasis on the existence of strong solutions with an idea of a proof