scholarly journals Numerical preservation issues in stochastic dynamical systems by $ \vartheta $-methods

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Raffaele D'Ambrosio ◽  
Stefano Di Giovacchino
Keyword(s):  
Monte Carlo ◽  
Dynamical Systems ◽  
Theoretical Analysis ◽  
Monte Carlo Simulations ◽  
Duffing Oscillator ◽  
Stochastic Dynamical Systems ◽  
Numerical Evidence ◽  
Stochastic Oscillator ◽  
Expected Values

<p style='text-indent:20px;'>This paper analyzes conservation issues in the discretization of certain stochastic dynamical systems by means of stochastic <inline-formula><tex-math id="M2">\begin{document}$ \vartheta $\end{document}</tex-math></inline-formula>-mehods. The analysis also takes into account the effects of the estimation of the expected values by means of Monte Carlo simulations. The theoretical analysis is supported by a numerical evidence on a given stochastic oscillator, inspired by the Duffing oscillator.</p>

KINETIC ROUGHENING AND INTERACTING REACTING SPECIES: NONLINEAR ASPECTS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 470-474 ◽  
Author(s):  
I.M. SOKOLOV ◽  
P. ARGYRAKIS ◽  
A. BLUMEN
Keyword(s):  
Monte Carlo ◽  
Theoretical Analysis ◽  
Diffusion Process ◽  
Monte Carlo Simulations ◽  
Short Range ◽  
Reaction Diffusion ◽  
Kinetic Roughening ◽  
Constant Rate ◽  
Good Agreement

We consider the A+B→0 reaction, in which particles interact through short-range forces. The analysis leads to expressions akin in form to those which describe kinetic roughening. In a situation in which particles are generated with a constant rate j0, their concentration n(t) grows as [Formula: see text] in d=1. Here the theoretical analysis predicts γ=1/5 and β=2/5, in very good agreement with direct Monte-Carlo simulations of the reaction-diffusion process.

scholarly journals Dependency of regret on accuracy of variance estimation for different versions of UCB strategy for Gaussian multi-armed bandits

2021 ◽  
Vol 2052 (1) ◽  
pp. 012013
Author(s):  
S V Garbar
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Estimation ◽  
Estimation Error ◽  
Continuous Functions ◽  
Confidence Bound ◽  
Expected Values ◽  
Upper Confidence Bound

Abstract We consider two variations of upper confidence bound strategy for Gaussian two-armed bandits. Rewards for the arms are assumed to have unknown expected values and unknown variances. It is demonstrated that expected regret values for both discussed strategies are continuous functions of reward variance. A set of Monte-Carlo simulations was performed to show the nature of the relation between variance estimation and losses. It is shown that the regret grows only slightly when the estimation error is fairly large, which allows to estimate the variance during the initial steps of the control and stop this estimation later.

scholarly journals Comparison of straight line curve fit approaches for determining parameter variances and covariances

2020 ◽  
Vol 11 ◽  
pp. 14
Author(s):  
Vishal Ramnath
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Applied Pressure ◽  
Ordinary Least Squares ◽  
Pressure Balance ◽  
Straight Line ◽  
Covariance Term ◽  
Expected Values

Pressure balances are known to have a linear straight line equation of the form y = ax + b that relates the applied pressure x to the effective area y, and recent work has investigated the use of Ordinary Least Squares (OLS), Weighted Least Squares (WLS), and Generalized Least Squares (GLS) regression schemes in order to quantify the expected values of the zero-pressure area A0 = b and distortion coefficient λ = a/b in pressure balance models of the form y = A0(1 + λx). The limitations with conventional OLS, WLS and GLS approaches is that whilst they may be used to quantify the uncertainties u(a) and u(b) and the covariance cov(a, b), it is technically challenging to analytically quantify the covariance term cov(A0, λ) without additional Monte Carlo simulations. In this paper, we revisit an earlier Weighted Total Least Squares with Correlation (WTLSC) algorithm to determine the variances u2(a) and u2(b) along with the covariance cov(a, b), and develop a simple analytical approach to directly infer the corresponding covariance cov(A0, λ) for pressure metrology uncertainty analysis work. Results are compared to OLS, WLS and GLS approaches and indicate that the WTLSC approach may be preferable as it avoids the need for Monte Carlo simulations and additional numerical post-processing to fit and quantify the covariance term, and is thus simpler and more suitable for industrial metrology pressure calibration laboratories. Novel aspects is that a Gnu Octave/Matlab program for easily implementing the WTLSC algorithm to calculate parameter expected values, variances and covariances is also supplied and reported.

scholarly journals Dual-Polarized Planar Phased Array Analysis for Meteorological Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Chen Pang ◽  
Peter Hoogeboom ◽  
François Le Chevalier ◽  
Herman W. J. Russchenberg ◽  
Jian Dong ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Measurement Error ◽  
Theoretical Analysis ◽  
Monte Carlo Simulations ◽  
Phased Array ◽  
Antenna Element ◽  
Array Analysis ◽  
Dual Polarized ◽  
Dual Polarized Antenna ◽  
Entire Array

This paper presents a theoretical analysis for the accuracy requirements of the planar polarimetric phased array radar (PPPAR) in meteorological applications. Among many factors that contribute to the polarimetric biases, four factors are considered and analyzed in this study, namely, the polarization distortion due to the intrinsic limitation of a dual-polarized antenna element, the antenna pattern measurement error, the entire array patterns, and the imperfect horizontal and vertical channels. Two operation modes, the alternately transmitting and simultaneously receiving (ATSR) mode and the simultaneously transmitting and simultaneously receiving (STSR) mode, are discussed. For each mode, the polarimetric biases are formulated. As the STSR mode with orthogonal waveforms is similar to the ATSR mode, the analysis is mainly focused on the ATSR mode and the impacts of the bias sources on the measurement of polarimetric variables are investigated through Monte Carlo simulations. Some insights of the accuracy requirements are obtained and summarized.

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