The course gives an introduction to stochastic processes and their applications in natural sciences. We start with the development of a probabilistic description of stochastic processes, which allows us then to 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.

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

further readingr:
Dynkin: Markov processes (Springer, 1965)
Feller: Probability Theory and Its Applications, vol. 1 + 2 (Wiley, 1968-1971)
Kallenberg: Foundations of modern probability (Springer, 2002)