Simulation and analysis of stochastic signals using the Kolmogorov-Feller equation

We consider a Green´s function solution to the Classical Kolmogorov-Feller Equation which requires an iterative approach for which a sufficient convergence condition is derived. The solution obtained is applied to the simulation of signals whose spectral properties are determined by a Characteristic Function of the form k -q where k is the spatial frequency and q is the `Fourier Dimension´. Using example macroeconomic financial time series (FTSE Close-of-Day and the Dow Jones Industrial Average), correlations are observed to exist between q and long term trends in the series using a standard moving window process. This result provides the potential for developing an accurate short term forecasting strategy.