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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 j k j��q; q > 0 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.
Blackledge, J. et al. (2012) Simulation and Analysis of Stochastic Signals using the Kolmogorov-Feller Equation. Irish Signals and Systems Conference, 2012, NUI Maynooth, 2012.doi:10.1049/ic.2012.0168