Random walks (Mathematics), Differential equations, Monte Carlo method
In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a diffusion process in the sense of distributions is proved. Simulations based upon multi-term fractional order differential equations are performed.
Andries, Erik; Umarov, Sabir; and Steinberg, Stanly, "Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications in Cell Biology" (2006). Mathematics Faculty Publications. 15.
Andries, Erik & Umarov, Sabir & Steinberg, Stanly. (2006). Monte Carlo random walk simulations based on distributed order differential equations with applications to cell biology. Fractional Calculus and Applied Analysis, 9(4), 351–369.