PERIODICITY AS CONDITION TO NOISE ROBUSTNESS FOR CHAOTIC MAPS WITH PIECEWISE CONSTANT INVARIANT DENSITY

2006 ◽  
Vol 16 (11) ◽  
pp. 3391-3400 ◽  
Author(s):  
FABIO PARESCHI ◽  
RICCARDO ROVATTI ◽  
GIANLUCA SETTI
Keyword(s):  
General Class ◽  
Chaotic Maps ◽  
Random Variable ◽  
Noise Robustness ◽  
Invariant Density ◽  
Piecewise Constant ◽  
First Order ◽  
Additive Map ◽  
External Perturbations ◽  
Practical Concern

Chaotic maps represent an effective method of generating random-like sequences, that combines the benefits of relying on simple, causal models with good unpredictability. However, since chaotic maps behavior is generally strongly dependent on unavoidable implementation errors and external perturbations, the possibility of guaranteeing map statistical robustness is of great practical concern. Here we present a technique to guarantee the independence of the first-order statistics of external perturbations, modeled as an additive, map-independent random variable. The developed criterion applies to a quite general class of maps.

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

2013 ◽  
Vol 16 (04) ◽  
pp. 1350029
Author(s):  
SHIH-FENG HUANG ◽  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
Characteristic Function ◽  
Path Integral ◽  
Unit Root ◽  
Autoregressive Model ◽  
Integral Method ◽  
Unit Root Test ◽  
Random Variable ◽  
Limiting Distribution ◽  
First Order ◽  
Path Integral Method

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

scholarly journals MATHEMATICAL MODEL AND EXPERIMENTAL PROCEEDINGS TO DETERMINE ROLL WAVES IN OPEN CHANNELS

2011 ◽  
Vol 10 (1-2) ◽  
pp. 55
Author(s):  
G. H. Fiorot ◽  
G. F. Maciel ◽  
C. Kitano
Keyword(s):  
Experimental Approach ◽  
Clean Water ◽  
Photometric System ◽  
First Order ◽  
Blood Flows ◽  
External Perturbations ◽  
Roll Waves ◽  
Experimental Project ◽  
Representative Model ◽  
Absorption Technique

The goal of this paper is consolidate a representative model previously developed by RMVP team (Rheological Studies on Viscous and Viscousplastic Materials) from UNESP - Ilha Solteira, for a typical phenomenonthat occurs on spillways, river's bed, landslides, mudflows, blood flows, for Newtonian and non-Newtonian fluids, known as roll waves. Another goal of this paper is present an experimental project designed for capturing measurements (amplitude and wavelength) of these instabilities. From a mathematical perspective, a first-order analytical model is showed, based on Cauchy's equations system, once developed by the team (Ferreira, 2007), which provides a generation condition for roll waves through temporal linear stability analysis. This model follows the remarkable work of Dressler (1949) and it is able to generate roll waves for many rheological configurations, from Newtonian to Herschel & Bulkley models, representing clean water up to muddy mixtures, respectively. A numerical routine developed in Matlab/Simulink is used to show some results that illustrate roll waves pattern. Due to the lack of roll waves data (amplitude and wavelength), the team started to focus on the experimental approach of the phenomenon, aiming to design an apparatus that would be capable to reproduce roll waves in special conditions of flow, isolated from external perturbations. This project is here presented along with a proposal of a photometric system to ascertain measures of the flow height through light absorption technique, based on experiments found in the literature. The final execution of this experiment and the correct obtaining of amplitude and wavelength will contribute for the validation of the model here presented.

scholarly journals Nonrecurrence and Bell-like inequalities

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 762-768
Author(s):  
Douglas G. Danforth
Keyword(s):  
Infinite Number ◽  
General Class ◽  
Hidden Variables ◽  
Random Variables ◽  
Random Variable ◽  
Bell Inequalities ◽  
Usual Sense ◽  
Real Random Variable ◽  
Action At A Distance ◽  
The Continuum

AbstractThe general class,Λ, of Bell hidden variables is composed of two subclassesΛRandΛNsuch thatΛR⋃ΛN=ΛandΛR∩ΛN= {}. The classΛNis very large and contains random variables whose domain is the continuum, the reals. There are an uncountable infinite number of reals. Every instance of a real random variable is unique. The probability of two instances being equal is zero, exactly zero.ΛNinduces sample independence. All correlations are context dependent but not in the usual sense. There is no “spooky action at a distance”. Random variables, belonging toΛN, are independent from one experiment to the next. The existence of the classΛNmakes it impossible to derive any of the standard Bell inequalities used to define quantum entanglement.

Reliability Methods for Bimodal Distribution With First-Order Approximation1

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Probability Density ◽  
Order Approximation ◽  
Limit State ◽  
Random Variables ◽  
Random Variable ◽  
State Function ◽  
First Order ◽  
Reliability Method ◽  
Reliability Methods ◽  
Basic Random Variable

In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.

Dynamic Reliability Evaluation by First-Order Reliability Method Integrated with Stochastic Pseudo Excitation Method

2020 ◽  
pp. 2150024
Author(s):  
Siyu Zhu ◽  
Tianyu Xiang
Keyword(s):  
Random Variable ◽  
Random Excitation ◽  
Pseudo Excitation Method ◽  
First Order Reliability Method ◽  
Dynamic Reliability ◽  
First Order ◽  
Reliability Method ◽  
Uncertain Structure ◽  
Pseudo Excitation ◽  
Excitation Method

The stochastic pseudo excitation method (SPEM), which is based on the principle of pseudo excitation method (PEM), is introduced to represent the randomness of dynamic input in which the amplitude of excitation is adopted as a random variable. Based on the mathematic definition of power spectral density, a physical interpolation of the SPEM is discussed. Even if one random variable is involved in calculation, the effects of the uncertainties are required to be investigated. The SPEM offers a simple but quite effective way to solve the dynamic reliability problem. Through integrating the new algorithm into first-order reliability method (FORM), the dynamic reliability of uncertain structure subjected to random excitation is studied. A linear oscillator with three types of white noise is adopted to verify the SPEM for dynamic reliability of linear random vibration analysis. Also, the accuracy and efficiency of SPEM to handle the multi-degree-of-freedom structure is investigated in this paper.

On a functional equation for general branching processes

1973 ◽  
Vol 10 (1) ◽  
pp. 198-205 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Functional Equation ◽  
Integral Equation ◽  
Population Size ◽  
General Class ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variable ◽  
Slow Variation ◽  
Age Dependent ◽  
Class Of Functions

If Z(t) denotes the population size in a Bellman-Harris age-dependent branching process such that a non-denenerate random variable W, then it is known that E(W) = 1 and that ϕ (u) = E(e–uW) satisfies a well-known integral equation. In this situation Athreya [1] has recently found a NASC for E(W |log W| y) <∞, for γ > 0. This paper generalizes Athreya's results in two directions. Firstly a more general class of branching processes is considered; secondly conditions are found for E(W 1 + βL(W)) < ∞ for 0 β < 1, where L is one of a class of functions of slow variation.

A Note on Nonparametric Estimation of the CTE

2009 ◽  
Vol 39 (2) ◽  
pp. 717-734 ◽  
Author(s):  
Bangwon Ko ◽  
Ralph P. Russo ◽  
Nariankadu D. Shyamalkumar
Keyword(s):  
Order Term ◽  
Random Variable ◽  
Small Samples ◽  
Closed Form Expression ◽  
Form Expression ◽  
Continuous Random Variable ◽  
Underlying Distribution ◽  
First Order ◽  
Bootstrap Approach ◽  
Conditional Tail Expectation

AbstractThe α-level Conditional Tail Expectation (CTE) of a continuous random variable X is defined as its conditional expectation given the event {X > qα} where qα represents its α-level quantile. It is well known that the empirical CTE (the average of the n (1 – α) largest order statistics in a sample of size n) is a negatively biased estimator of the CTE. This bias vanishes as the sample size increases, but in small samples can be significant. In this article it is shown that an unbiased nonparametric estimator of the CTE does not exist. In addition, the asymptotic behavior of the bias of the empirical CTE is studied, and a closed form expression for its first order term is derived. This expression facilitates the study of the behavior of the empirical CTE with respect to the underlying distribution, and suggests an alternative (to the bootstrap) approach to bias correction. The performance of the resulting estimator is assessed via simulation.

scholarly journals Ordinary differential systems describing hysteresis effects and numerical simulations

2002 ◽  
Vol 7 (11) ◽  
pp. 563-583 ◽  
Author(s):  
Emil Minchev ◽  
Takanobu Okazaki ◽  
Nobuyuki Kenmochi
Keyword(s):  
Numerical Simulations ◽  
General Class ◽  
Uniqueness Result ◽  
Input Output ◽  
Nonlinear Odes ◽  
Differential Systems ◽  
Subdifferential Operator ◽  
First Order

We consider a general class of ordinary differential systems which describes input-output relations of hysteresis types, for instance, play or stop operators. The system consists of two first-order nonlinear ODEs and one of them includes a subdifferential operator depending on the unknowns. Our main objective of this paper is to give an existence-uniqueness result for the system as well as to give various numerical simulations of input-output relations which the system describes as typical cases.

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