The dynamics of many systems in nature is too complicated to be described ab initio. Today, the investigation of such complex systems plays an important role, not only in physics, but in many fields of science. In general, such systems are in a state far from equilibrium, i. e. they are exposed to a constant flux of energy. Therefore, a common feature of complex systems is the occurrence of intricate fluctuations which can be induced either by a complex environment or stem from internal dynamics. To describe these systems, one applies the mathematical theory of stochastic processes. The research interests of our group range from the application of stochastic processes to biological, ecological and socio-economic systems to the mathematical generalization of stochastic processes to account for systems which exhibit anomalous diffusion. Thereby an interdisciplinary approach is employed, applying methods from statistical mechanics, network theory and game theory.