Volume 28, Issue 1

In this paper, we present and study highly efficient stochastic methods, including optimal super convergent methods for multidimensional sensitivity analysis of large-scale ecological models and digital twins. The computational efficiency (in terms of relative error and computational time) of the stochastic algorithms for multidimensional numerical integration has been studied to analyze the sensitivity of the digital ecosystem, namely the UNI-DEM model, which is particularly appropriate for connecting and orchestrating the many autonomous systems, infrastructures, platforms and data that constitute the bedrock of predicting and analyzing the consequences of possible climate changes. We deploy the digital twin paradigm in our consideration to study the output to variation of input emissions of the anthropogenic pollutants and to evaluate the rates of several chemical reactions.

We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of ℒ 2 {\mathcal{L}^{2}} -convergence of the truncated SD method and showed that it can be arbitrarily close to 1 2 {\frac{1}{2}} ; see [I. S. Stamatiou and N. Halidias, Convergence rates of the semi-discrete method for stochastic differential equations, Theory Stoch. Process. 24 2019, 2, 89–100]. We show that the truncated SD method is able to preserve the asymptotic stability of the underlying SDE. Motivated by a numerical example, we also propose a different SD scheme, using the Lamperti transformation to the original SDE. Numerical simulations support our theoretical findings.

We propose to apply the importance sampling and the antithetic variates statistical techniques to estimate steady-state quantities of an Hidden Markov chain (HMM) of which certain emissions are rarely generated. Compared to standard Monte Carlo simulation, the use of these techniques, allow a significant reduction in simulation time. Numerical Monte Carlo examples are studied to show the usefulness and efficiency of the proposed approach.

In this paper, we propose a recursive estimators of the regression function based on the two-time-scale stochastic approximation algorithms and the Bernstein polynomials. We study the asymptotic properties of this estimators. We compare the proposed estimators with the classic regression estimator using the Bernstein polynomial defined by Tenbusch. Results showed that, our proposed recursive estimators can overcome the problem of the edges associated with kernel regression estimation with a compact support. The proposed recursive two-time-scale estimators are compared to the non-recursive estimator introduced by Tenbusch and the performance of the two estimators are illustrated via simulations as well as two real datasets.

In this paper, we consider static parameter estimation for a class of continuous-time state-space models. Our goal is to obtain an unbiased estimate of the gradient of the log-likelihood (score function), which is an estimate that is unbiased even if the stochastic processes involved in the model must be discretized in time. To achieve this goal, we apply a doubly randomized scheme , that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization. Our novel estimate helps facilitate the application of gradient-based estimation algorithms, such as stochastic-gradient Langevin descent. We illustrate our methodology in the context of stochastic gradient descent (SGD) in several numerical examples and compare with the Rhee–Glynn estimator.

We address the problem of statistical simulation of a scalar real Gaussian random field inside the unit 3D ball. Two different methods are studied: (i) the method based on the known homogeneous isotropic power spectrum developed by Meschede and Romanowicz [M. Meschede and B. Romanowicz, Non-stationary spherical random media and their effect on long-period mantle waves, Geophys. J. Int. 203 2015, 1605–1625] and (ii) the method based on known radial and angular covariance functions suggested in this work. The first approach allows the extension of the simulation technique to the inhomogeneous or anisotropic case. However, the disadvantage of this approach is the lack of accurate statistical characterization of the results. The accuracy of considered methods is illustrated by numerical tests, including a comparison of the estimated and analytical covariance functions. These methods can be used in many applications in geophysics, geodynamics, or planetary science where the objective is to construct spatial realizations of 3D random fields based on a statistical analysis of observations collected on the sphere or within a spherical region.