Given a geometric Brownian motion S=(St)t[set membership, variant][0,T] and a Borel measurable function such that g(ST)[set membership, variant]L2, we approximate bywhere 0=[tau]0[less-than-or-equals, slant]...[less-than-or-equals, slant][tau]n=T is an increasing sequence of stopping times and...

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...

This paper approximates stochastic integrals with respect to the geometric Brownian motion by stochastic integrals over discretized integrands, where deterministic, but not necessarily equidistant, time nets are used.

In the research project "MetPVNet", both, the forecast-based operation management in distribution grids and as well as the forecasts of the feed-in of PV-power from decentralized plants could be improved on the basis of satellite data and numerical weather forecasts. Based on a detailed network...

In the research project "MetPVNet", both, the forecast-based operation management in distribution grids and as well as the forecasts of the feed-in of PV-power from decentralized plants could be improved on the basis of satellite data and numerical weather forecasts. Based on a detailed network...

We study the problem of estimating the coefficients of a diffusion (Xl, t 2: 0); the estimation is based on discrete data Xn . . n = 0, 1, ... ,N. The sampling frequency delta t is constant , and asymptotics arc taken at the number of observations tends to infinity. We prove that the problem of...