Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, and Steinberg, Stanly. "Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology." Fractional Calculus and Applied Analysis 9.4 (2006): 351-369. <http://eudml.org/doc/11288>.

@article{Andries2006,
abstract = {Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In 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.},
author = {Andries, Erik, Umarov, Sabir, Steinberg, Stanly},
journal = {Fractional Calculus and Applied Analysis},
keywords = {65C05; 60G50; 39A10; 92C37},
language = {eng},
number = {4},
pages = {351-369},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology},
url = {http://eudml.org/doc/11288},
volume = {9},
year = {2006},
}

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
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 4
SP - 351
EP - 369
AB - Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In 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.
LA - eng
KW - 65C05; 60G50; 39A10; 92C37
UR - http://eudml.org/doc/11288
ER -