Stochastic Analysis

  A blackboard showing the Wiener-Ito formula Copyright: © private

Stochastic Analysis is a course in the bachelor's curriculum. The students will develop familiarity and capability with problems and tools of stochastic analysis and diffusion processes. In addition, students will develop an understanding of connections between probability/stochastics and analysis/PDE.


Modes of convergence of probability measures; tightness of probability measures; Brownian motion and its properties; stopping times and strong Markov property; martingale property and martingale convergence theorems; Ito integral; diffusion processes; large deviation principles.


In order to take the course, students must have passed the modules Analysis I, II, III, and Stochastics I. They also need some knowledge of Functional Analysis.


Students are required to pass a written or oral exam. Type and duration of the assessment will be announced at the beginning of the course.


  1. K. L. Chung: A Course in Probability Theory
  2. Karatzas and Shreve: Brownian Motion and Stochastic Calculus.
  3. Revuz and Yor: Continuous Martingales and Brownian Motion.