This thesis introduces an Ornstein-Uhlenbeck model by a stochastic integral rep-resentation where the driving stochastic process is a fractional Lévy process (FLP). Since FLPs are in general not semimartingales, pathwise Riemann-Stieltjes inte- gration can be applied. This works quite well for differentiable integrands such as in the Ornstein-Uhlenbeck case. To achieve the convergence of improper in-tegrals the long time behavior of FLPs is derived. This is sufficient to define the fractional Lévy Ornstein-Uhlenbeck process (FLOUP) pathwise as an improper Riemann-Stieltjes integral. As one would expect there is also a close relation to stochastic differential equations: We show that the FLOUP is the unique stationary solution of the corresponding Langevin equation. Furthermore we calculate the autocovariance function of a FLOUP and prove that its increments exhibit long range dependence. So far only integration of deterministic differentiable integrands has been considered. However when one wants to look at more general stochastic differential equations it is clear that pathwise Riemann-Stieltjes integration becomes more difficult. We therefore invoke a generalization of the concept of bounded variation and restrict ourselves to FLPs whose sample paths are in that class. It is then possible to prove a chain rule and density formula as known from classical Riemann-Stieltjes calculus. Finally we look at stochastic differential equations driven by FLPs and present conditions on the coeficient functions such that solutions can be constructed from the corresponding FLOUP. In fact stationary solutions are obtained by monotone trans- formation of the FLOUP.     «

This thesis introduces an Ornstein-Uhlenbeck model by a stochastic integral rep-resentation where the driving stochastic process is a fractional Lévy process (FLP). Since FLPs are in general not semimartingales, pathwise Riemann-Stieltjes inte- gration can be applied. This works quite well for differentiable integrands such as in the Ornstein-Uhlenbeck case. To achieve the convergence of improper in-tegrals the long time behavior of FLPs is derived. This is sufficient to define the fractional L...     »