Approximate and generalized confidence bands for the mean and mode functions of the lognormal diffusion process

2007 ◽  
Vol 51 (8) ◽  
pp. 4038-4053 ◽  
Author(s):  
R. Gutiérrez ◽  
N. Rico ◽  
P. Román ◽  
F. Torres
Keyword(s):  
Diffusion Process ◽  
Confidence Bands ◽  
The Mean ◽  
Lognormal Diffusion Process

scholarly journals Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

2021 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Transition Density ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Stochastic Diffusion ◽  
Life Expectancy At Birth ◽  
Transition Density Function ◽  
Lognormal Diffusion Process ◽  
Trend Functions

A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

Non-Markovian effect of the fractional damping environment and Newton’s second law of motion

2018 ◽  
Vol 32 (19) ◽  
pp. 1850210
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qin ◽  
Yu-Qing Xu ◽  
Shu-Qin Lv ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Mean Square Displacement ◽  
Dynamical Analysis ◽  
Second Law ◽  
Mean Square ◽  
Fractional Damping ◽  
Dynamical Mechanism ◽  
Brownian Particles ◽  
The Mean ◽  
Dissipative Environments

We report, in this paper, a recent study on the dynamical mechanism of Brownian particles diffusing in the fractional damping environment, where several important quantities such as the mean square displacement (MSD) and mean square velocity are calculated for dynamical analysis. A particular type of backward motion is found in the diffusion process. The reason of it is analyzed intrinsically by comparing with the diffusion in various dissipative environments. Results show that the diffusion in the fractional damping environment obeys the Langevin dynamics which is quite different form what is expected.

scholarly journals Diffusion-Scale Tightness of Invariant Distributions of a Large-Scale Flexible Service System

2015 ◽  
Vol 47 (01) ◽  
pp. 251-269 ◽  
Author(s):  
A. L. Stolyar
Keyword(s):  
Diffusion Process ◽  
Service Time ◽  
Large Scale ◽  
Service System ◽  
Arrival Rate ◽  
Asymptotic Regime ◽  
Invariant Distributions ◽  
Multiple Customer Classes ◽  
The Mean ◽  
Diffusion Scale

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routeing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a leaf activity priority (LAP) policy, introduced by Stolyar and Yudovina (2012). An asymptotic regime is considered, where the arrival rate of customers and number of servers in each pool tend to ∞ in proportion to a scaling parameter r, while the overall system load remains strictly subcritical. We prove tightness of diffusion-scaled (centered at the equilibrium point and scaled down by r −1/2) invariant distributions. As a consequence, we obtain a limit interchange result: the limit of diffusion-scaled invariant distributions is equal to the invariant distribution of the limiting diffusion process.

Defect Diffusion Models in NMR and Dielectric Relaxation

1978 ◽  
Vol 33 (11) ◽  
pp. 1294-1306 ◽  
Author(s):  
Rainer Kimmich ◽  
Gerhard Voigt
Keyword(s):  
Diffusion Process ◽  
Dielectric Relaxation ◽  
Diffusion Models ◽  
Defect Concentration ◽  
Relaxation Behaviour ◽  
Defect Diffusion ◽  
Rotational Isomers ◽  
Mean Lifetime ◽  
The Mean

The effect of diffusing defects such as vacancies, displacements, torsions, and rotational isomers on the nmr and dielectric relaxation behaviour is treated under various aspects. The influences of the dimensionality of the diffusion process, of the mutual hindrance, of the defect concentration, of the defect length and of the mean lifetime are derived and discussed.

scholarly journals Diffusion-Scale Tightness of Invariant Distributions of a Large-Scale Flexible Service System

2015 ◽  
Vol 47 (1) ◽  
pp. 251-269 ◽  
Author(s):  
A. L. Stolyar
Keyword(s):  
Diffusion Process ◽  
Service Time ◽  
Large Scale ◽  
Service System ◽  
Arrival Rate ◽  
Asymptotic Regime ◽  
Invariant Distributions ◽  
Multiple Customer Classes ◽  
The Mean ◽  
Diffusion Scale

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routeing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a leaf activity priority (LAP) policy, introduced by Stolyar and Yudovina (2012). An asymptotic regime is considered, where the arrival rate of customers and number of servers in each pool tend to ∞ in proportion to a scaling parameter r, while the overall system load remains strictly subcritical. We prove tightness of diffusion-scaled (centered at the equilibrium point and scaled down by r−1/2) invariant distributions. As a consequence, we obtain a limit interchange result: the limit of diffusion-scaled invariant distributions is equal to the invariant distribution of the limiting diffusion process.

Baldcypress height–diameter equations and their prediction confidence intervals

1992 ◽  
Vol 22 (9) ◽  
pp. 1429-1434 ◽  
Author(s):  
Bernard R. Parresol
Keyword(s):  
United States ◽  
Confidence Intervals ◽  
Nonlinear Regression ◽  
Basal Area ◽  
Confidence Bands ◽  
Bald Cypress ◽  
Prediction Confidence ◽  
Independent Variable ◽  
The Mean ◽  
Stand Basal Area

Height–diameter relationships are an important component in yield estimation, stand description, and damage appraisals. A nonlinear exponential function used extensively in the northwest United States was chosen for bald cypress (Taxodiumdistichum (L.) Rich.). Homogeneity and normality of residuals were examined, and the function as well as the mean and individual prediction confidence bands were plotted. The inclusion of stand basal area as an additional independent variable provided a better fit to the data. The paper is concluded with a section on construction and use of simple and joint confidence intervals about the mean and individual predictions from the nonlinear regression.

A NEW PROCEDURE FOR RAPIDLY ESTIMATING EUROPEAN PINE SAWFLY (HYMENOPTERA: DIPRIONIDAE) POPULATION LEVELS IN YOUNG PINE PLANTATIONS

1971 ◽  
Vol 103 (9) ◽  
pp. 1315-1322 ◽  
Author(s):  
Louis F. Wilson ◽  
Douglas J. Gerrard
Keyword(s):  
Negative Binomial ◽  
Confidence Bands ◽  
Pine Plantations ◽  
Scotch Pine ◽  
Simple Criterion ◽  
Pine Sawfly ◽  
Insect Populations ◽  
The Mean ◽  
European Pine Sawfly ◽  
Image Position

AbstractA method is proposed for rapidly estimating the population levels of European pine sawfly in young red and Scotch pine plantations. On the hypothesis that the numbers of larval colonies per tree are distributed within a stand according to a negative binomial series, it is shown that an estimate Y of the mean sawfly count per tree in any relevant pine stand may be predicted from knowledge of the proportion p of trees infested, by means of the equationin which k is an estimate of a distribution parameter. The estimate k is derived beforehand, by Maximum Likelihood from a series of insect populations representative of those in which predictions are contemplated.Approximate 95% confidence limits for estimated densities are computed from a variance estimator reflecting two sources of error. The plotted confidence bands pertaining to samples of various size furnish a simple criterion for judging directly from the proportion of infested trees whether or not suppression measures are needed in a plantation.

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