Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
نویسندگان
چکیده
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. Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37
منابع مشابه
Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations
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. Mathematics ...
متن کاملAn equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable, quantitatively-accurate, individual-level model. However, important problems in areas ranging from ecology to medicine involve large collections of individu...
متن کاملNew Tests of Random Numbers for Simulations in Physical Systems
The aim of this Thesis is to present five new tests for random numbers, which are widely used e.g. in computer simulations in physics applications. The first two tests, the cluster test and the autocorrelation test, are based on analogies to the two-dimensional Ising model. The next two, the random walk test and the n-block test, are based on studies of random walks, and the condition number te...
متن کاملPerformance Evaluation of Generalized Polynomial Chaos
In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos...
متن کاملNonlinear Monte Carlo Estimators for Parabolic Equation
We consider the parabolic type equation with a source-sink term and construct the Monte Carlo estimator for it. The procedure is based on the Hopf-Cole transformation and a Monte Carlo estimator for the correspondent Burgers equation. Monte Carlo estimators for the heat and diffusion equations are very well known since the first steps of the method. The algorithms are based usually on the intim...
متن کامل