Geodesic
Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
Fractional calculus and applied analysis, Tome 9 (2006) no. 4, pp. 351-369.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: Random Walk, Anomalous Diffusion, Confined Diffusion, Distributed Order Differential Equation, Monte-Carlo Simulation, 65C05, 60G50, 39A10, 92C37 
@article{FCAA_2006_9_4_a2,
     author = {Andries, Erik and Umarov, Sabir and Steinberg, Stanly},
     title = {Monte {Carlo} {Random} {Walk} {Simulations} {Based} on {Distributed} {Order} {Differential} {Equations} with {Applications} to {Cell} {Biology}},
     journal = {Fractional calculus and applied analysis},
     pages = {351--369},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a2/}
}
TY  - JOUR
AU  - Andries, Erik
AU  - Umarov, Sabir
AU  - Steinberg, Stanly
TI  - Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
JO  - Fractional calculus and applied analysis
PY  - 2006
SP  - 351
EP  - 369
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a2/
LA  - en
ID  - FCAA_2006_9_4_a2
ER  - 
%0 Journal Article
%A Andries, Erik
%A Umarov, Sabir
%A Steinberg, Stanly
%T Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
%J Fractional calculus and applied analysis
%D 2006
%P 351-369
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a2/
%G en
%F FCAA_2006_9_4_a2
Andries, Erik; Umarov, Sabir; Steinberg, Stanly. Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology. Fractional calculus and applied analysis, Tome 9 (2006) no. 4, pp. 351-369. http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a2/