Une généralisation du modèle de diffusion de Bernoulli–Laplace

1996 ◽  
Vol 33 (3) ◽  
pp. 688-697
Author(s):  
Djaouad Taïbi
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Asymptotic Approximation ◽  
Legendre Polynomials ◽  
Transition Density ◽  
Second Stage ◽  
Classical Scheme ◽  
The Mean ◽  
Laplace Diffusion

A generalization of the Bernoulli–Laplace diffusion model is proposed. We consider the case where the number of balls exchanged is greater than one. We show that the stationary distribution is the same as in the classical scheme and we give the mean and the variance of the process. In a second stage, we study the asymptotic approximation based on the diffusion process. A solution of transition density is given using Legendre polynomials.

Une généralisation du modèle de diffusion de Bernoulli–Laplace

1996 ◽  
Vol 33 (03) ◽  
pp. 688-697
Author(s):  
Djaouad Taïbi
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Asymptotic Approximation ◽  
Legendre Polynomials ◽  
Transition Density ◽  
Second Stage ◽  
Classical Scheme ◽  
The Mean ◽  
Laplace Diffusion

A generalization of the Bernoulli–Laplace diffusion model is proposed. We consider the case where the number of balls exchanged is greater than one. We show that the stationary distribution is the same as in the classical scheme and we give the mean and the variance of the process. In a second stage, we study the asymptotic approximation based on the diffusion process. A solution of transition density is given using Legendre polynomials.

The infinitely-many-neutral-alleles diffusion model

1981 ◽  
Vol 13 (03) ◽  
pp. 429-452 ◽  
Author(s):  
S. N. Ethier ◽  
Thomas G. Kurtz
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Order Statistics ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Stochastic Models ◽  
Dirichlet Distribution ◽  
Infinite Dimensional ◽  
Image Position ◽  
Discrete Stochastic Models

A diffusion process X(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown that X(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown that X(·) has a unique stationary distribution and is reversible and ergodic. Kingman's limit theorem for the descending order statistics of the symmetric Dirichlet distribution is obtained as a corollary.

The infinitely-many-neutral-alleles diffusion model

1981 ◽  
Vol 13 (3) ◽  
pp. 429-452 ◽  
Author(s):  
S. N. Ethier ◽  
Thomas G. Kurtz
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Order Statistics ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Stochastic Models ◽  
Dirichlet Distribution ◽  
Infinite Dimensional ◽  
Image Position ◽  
Discrete Stochastic Models

A diffusion process X(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown that X(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown that X(·) has a unique stationary distribution and is reversible and ergodic. Kingman's limit theorem for the descending order statistics of the symmetric Dirichlet distribution is obtained as a corollary.

Labour-use Efficiency of Assam Gramin Vikash Bank: Branch- and District-level Analysis

2021 ◽  
pp. 232102222110243
Author(s):  
Mohuya Deb Purkayastha ◽  
Joyeeta Deb ◽  
Ram Pratap Sinha
Keyword(s):  
Efficiency Score ◽  
Significant Variable ◽  
Data Envelopment ◽  
Tobit Regression ◽  
Second Stage ◽  
Time Period ◽  
Use Efficiency ◽  
The Mean ◽  
The Impact ◽  
Observation Period

The present study estimated labour-use efficiency of 48 branches of Assam Gramin Vikash Bank at its branch level, covering three districts of Barak Valley, which falls under Silchar region of the bank for the time period from 2010–2011 to 2017–2018. The study applied data envelopment analysis for estimating labour-use efficiency. In the second stage, the study applied censored Tobit regression for determining the impact of several contextual variables on efficiency. The study reveals that the mean labour-use efficiency score of the selected branches is 76% when averaged for the in-sample branches over the observation period. Results of the Tobit regression identified cluster 2 and total business of the branches as the significant factors for determining efficiency and the number of employees as a significant variable influencing inefficiency. JEL Classifications: G2, G20, G21, J3

scholarly journals Stochastic models for interference between searching insect parasites

1989 ◽  
Vol 30 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Phil Diamond
Keyword(s):  
Stationary Distribution ◽  
Intraspecific Competition ◽  
Death Process ◽  
Confluent Hypergeometric Functions ◽  
Large Populations ◽  
The Mean ◽  
The One ◽  
Globally Stable ◽  
Insect Parasites ◽  
Birth Death

AbstractCompetition between a finite number of searching insect parasites is modelled by differential equations and birth-death processes. In the one species case of intraspecific competition, the deterministic equilibrium is globally stable and, for large populations, approximates the mean of the stationary distribution of the process. For two species, both inter- and intraspecific competition occurs and the deterministic equilibrium is globally stable. When the birth-death process is reversible, it is shown that the mean of the stationary distribution is approximated by the equilibrium. Confluent hypergeometric functions of two variables are important to the theory.

A Two-Stage Combination Model for Wind Power Forecasting

2015 ◽  
Vol 737 ◽  
pp. 9-13
Author(s):  
Jun Zhang ◽  
Yuan Hao Wang ◽  
Ying Yi Li ◽  
Feng Guo
Keyword(s):  
Neural Network ◽  
Bp Neural Network ◽  
Wind Farm ◽  
General Trend ◽  
Two Stage ◽  
Combination Model ◽  
Second Stage ◽  
Combination Forecasting ◽  
The Mean ◽  
Power Sequence

With the wind farm data from the southeast coast this paper builds a two-stage combination forecasting model of output power based on data preprocessing which include filling up missing data and pre-decomposition. The first stage is a composite prediction of decomposed power sequence in which a time series and optimized BP neural network predict the general trend and the correlation of various factors respectively. The second stage is BP neural network with its input is the results of first stage. The effectiveness and accuracy of the two-stage combination model are verified by comparing the mean square error of the combination model and other models.

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 Experimental and Numerical Study on a Grouting Diffusion Model of a Single Rough Fracture in Rock Mass

2020 ◽  
Vol 10 (20) ◽  
pp. 7041
Author(s):  
Wenqi Ding ◽  
Chao Duan ◽  
Qingzhao Zhang
Keyword(s):  
Rock Mass ◽  
Diffusion Process ◽  
Diffusion Model ◽  
Numerical Study ◽  
Structural Characteristics ◽  
Analytical Formula ◽  
Diffusion Experiment ◽  
Cement Slurry ◽  
Temporal And Spatial Distribution ◽  
Rough Fracture

Grouting reinforcement is an important method used to solve problems encountered during tunnel construction, such as collapse and water gushing. The grouting diffusion process is greatly influenced by the structural characteristics of the fractures in a rock mass. First, an analytical grouting diffusion model of a single rough fracture under constant-pressure control is established based on the constitutive equation of a Bingham fluid. Second, the “quasi-elliptical” grouting diffusion pattern under the influence of roughness is revealed through a grouting diffusion experiment, which is conducted with an independently developed visualized testing apparatus. Furthermore, the analytical formula of roughness-corrected grouting diffusion characterized by the saw tooth density is established. Finally, an elaborate numerical simulation of the diffusion process of cement slurry (Bingham flow type) in a single rough fracture is carried out by introducing the Bingham–Papanastasiou rheological model. The temporal and spatial distribution characteristics of the velocity field and pressure field during the grouting diffusion process are analyzed as well. Moreover, the method and range of the roughness correction factor in the analytical grouting diffusion model are proposed based on the fracture roughness unit.

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