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

Andries, Erik; Umarov, Sabir; Steinberg, Stanly

Fractional Calculus and Applied Analysis (2006)

- Volume: 9, Issue: 4, page 351-369
- ISSN: 1311-0454

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topAndries, 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 -

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