Random Walk Anomalous Diffusion Confined Diffusion Distributed Order Differential Equation Monte-Carlo Simulation 65C05 60G50 39A10 92C37
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 9, No 4, (2006), 351p-369p
In this paper the multi-dimensional Monte-Carlo random walk simulation
models governed by distributed fractional order differential equations
(DODEs) and multi-term fractional order differential equations are constructed.
The construction is based on the discretization leading to a generalized
difference scheme (containing a finite number of terms in the time
step and infinite number of terms in the space step) of the Cauchy problem
for DODE. The scaling limits of the constructed random walks to a diffusion
process in the sense of distributions is proved.