Stochastic Process Generators¶
Karhunen-Loève expansion¶
This method samples stochastic processes using Karhunen-Loève expansion and is implemented in the class StocProc_KLE.
Setting up the class involves solving an eigenvalue problem which grows with the time interval the process is simulated on. Further generating a new process involves a multiplication with that matrix, therefore it scales quadratically with the time interval. Nonetheless it turns out that this method requires less random numbers than the Fast-Fourier method.
Fast-Fourier method¶
In the class StocProc_FFT a method based on Fast-Fourier transform is used to sample stochastic processes.
Setting up this class is quite efficient as it only calculates values of the associated spectral density. The number scales linear with the time interval of interest. However to achieve sufficient accuracy many of these values are required. As the generation of a new process is based on a Fast-Fouried-Transform over these values, this part is comparably lengthy.