title: Uncoupled continuous-time random walk model: analytical and numerical solutions.
abstract: Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
authors.affiliation: Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900, Maringá, Paraná, Brazil.
authors.forename: Kwok Sau
authors.initials: KS
authors.lastname: Fa
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008954:Models, Biological; D008956:Models, Chemical; D015233:Models, Statistical; D016011:Normal Distribution; D009716:Numerical Analysis, Computer-Assisted