Analysis of path properties of stochastic processes via generalized indices under allowance of time inhomogeneity

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Random phenomena which evolve in time are modeled mathematically via stochastic processes. The probabilistic symbol and the derived indices are used to analyze whether certain properties of the model coincide with the real world phenomenon. The theory developed until now is restricted to the time homogeneous case. This results in problems in the area of stochastic modeling, since temperature or asset prices do not evolve in a time homogeneous manner. Some models in mathematical finance and geology which allow for time inhomogeneity, cannot be analyzed by using the symbol and the indices. In order to allow for an easy and elegant way of analyzing such a bigger class of processes, we want to generalize the respective concepts and results. The results can be used in physics (Hausdorff dimension of the paths), numerics (approximation of solutions of stochastic differential equations) and mathematical finance (variation of the paths).