Search results for "Modelling"
showing 10 items of 1353 documents
On the derivation of a linear Boltzmann equation from a periodic lattice gas
2004
We consider the problem of deriving the linear Boltzmann equation from the Lorentz process with hard spheres obstacles. In a suitable limit (the Boltzmann-Grad limit), it has been proved that the linear Boltzmann equation can be obtained when the position of obstacles are Poisson distributed, while the validation fails, also for the "correct" ratio between obstacle size and lattice parameter, when they are distributed on a purely periodic lattice, because of the existence of very long free trajectories. Here we validate the linear Boltzmann equation, in the limit when the scatterer's radius epsilon vanishes, for a family of Lorentz processes such that the obstacles have a random distributio…
Updating input–output matrices: assessing alternatives through simulation
2009
A problem that frequently arises in economics, demography, statistics, transportation planning and stochastic modelling is how to adjust the entries of a matrix to fulfil row and column aggregation constraints. Biproportional methods in general and the so-called RAS algorithm in particular, have been used for decades to find solutions to this type of problem. Although alternatives exist, the RAS algorithm and its extensions are still the most popular. Apart from some interesting empirical and theoretical properties, tradition, simplicity and very low computational costs are among the reasons behind the great success of RAS. Nowadays computer hardware and software have made alternative proce…
Multiple smoothing parameters selection in additive regression quantiles
2021
We propose an iterative algorithm to select the smoothing parameters in additive quantile regression, wherein the functional forms of the covariate effects are unspecified and expressed via B-spline bases with difference penalties on the spline coefficients. The proposed algorithm relies on viewing the penalized coefficients as random effects from the symmetric Laplace distribution, and it turns out to be very efficient and particularly attractive with multiple smooth terms. Through simulations we compare our proposal with some alternative approaches, including the traditional ones based on minimization of the Schwarz Information Criterion. A real-data analysis is presented to illustrate t…
Stochastic model for the epitaxial growth of two-dimensional islands in the submonolayer regime
2016
The diffusion-based growth of islands composed of clusters of metal atoms on a substrate is considered in the aggregation regime. A stochastic approach is proposed to describe the dynamics of island growth based on a Langevin equation with multiplicative noise. The distribution of island sizes, obtained as a solution of the corresponding Fokker-Planck equation, is derived. The time-dependence of island growth on its fractal dimension is analysed. The effect of mobility of the small islands on the growth of large islands is considered. Numerical simulations are in a good agreement with theoretical results.
Spatio-temporal stochastic modelling: environmental and health processes
2010
Guest editorial
Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability
2006
Abstract Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.
Nonstationary distributions and relaxation times in a stochastic model of memristor
2020
We propose a stochastic model for a memristive system by generalizing known approaches and experimental results. We validate our theoretical model by experiments carried out on a memristive device based on multilayer structure. In the framework of the proposed model we obtain the exact analytic expressions for stationary and nonstationary solutions. We analyze the equilibrium and non-equilibrium steady-state distributions of the internal state variable of the memristive system and study the influence of fluctuations on the resistive switching, including the relaxation time to the steady-state. The relaxation time shows a nonmonotonic dependence, with a minimum, on the intensity of the fluct…
On an approximation problem for stochastic integrals where random time nets do not help
2006
Abstract Given a geometric Brownian motion S = ( S t ) t ∈ [ 0 , T ] and a Borel measurable function g : ( 0 , ∞ ) → R such that g ( S T ) ∈ L 2 , we approximate g ( S T ) - E g ( S T ) by ∑ i = 1 n v i - 1 ( S τ i - S τ i - 1 ) where 0 = τ 0 ⩽ ⋯ ⩽ τ n = T is an increasing sequence of stopping times and the v i - 1 are F τ i - 1 -measurable random variables such that E v i - 1 2 ( S τ i - S τ i - 1 ) 2 ∞ ( ( F t ) t ∈ [ 0 , T ] is the augmentation of the natural filtration of the underlying Brownian motion). In case that g is not almost surely linear, we show that one gets a lower bound for the L 2 -approximation rate of 1 / n if one optimizes over all nets consisting of n + 1 stopping time…
Estimating growth charts via nonparametric quantile regression: a practical framework with application in ecology.
2013
We discuss a practical and effective framework to estimate reference growth charts via regression quantiles. Inequality constraints are used to ensure both monotonicity and non-crossing of the estimated quantile curves and penalized splines are employed to model the nonlinear growth patterns with respect to age. A companion R package is presented and relevant code discussed to favour spreading and application of the proposed methods.
Volatility in Financial Markets: Stochastic Models and Empirical Results
2002
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fails in describing the empirical pdf over a moderately large volatility range.