This course is the sequel of the course of Stochastics I. The main objective is to build upon the concepts developed in Stochastics I and introduce stochastic processes, which are an important modeling tool for a wide range of applications across science and technology. We begin with the development of a probabilistic description of stochastic processes, which allows us to eventually introduce Gaussian processes and Markov chains. The "microscopic" counterpart to this description are stochastic differential equations, which provide us with representations of the random paths of many continuous processes. An important class are diffusion processes with their numerous applications.

relevant references (in alphabetical order):

• Gardiner: Handbook of Stochastic Methods (Springer, 2004)
• Klenke: Wahrscheinlichkeitstheorie (Springer, 2013)
• Meintrup & Schäffler: Stochastik (Springer, 2005)
• Øksendal: Stochastic Differential Equations (Springer, 2010)
• van Kampen: Stochastic Processes in Physics and Chemistry (Elsevier, 2007)

further reading:

• Bauer: Probability Theory (De Gruyter, 1996)
• Dynkin: Markov processes (Springer, 1965)
• Feller: Probability Theory and Its Applications, Bd. 1 und 2 (Wiley, 1968-1971)
• Kallenberg: Foundations of modern probability (Springer, 2002)

Requirements: previous courses in analysis and probability theory (Stochastics I) are necessary.