Joint probability distributions and multipoint correlations of the continuous-time random walk.
We present an efficient method to determine the Fourier-Laplace transform of the joint n-point probability distribution of a continuous-time random walk for arbitrary finite n. Additionally, we devise a recursive procedure with which it is possible to calculate the Laplace transforms of the multipoint correlation functions without having to determine the joint probability distributions first. The methods are used on several examples with both independent and dependent distributions for the waiting time and the spatial step size.
Niemann
Markus
M
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany. niemann@mpipks-dresden.mpg.de
Kantz
Holger
H