Simulation of random effects in transmission line models via stochastic differential equations

2012 ◽  
Author(s):  
Lubomir Brancik ◽  
Ales Prokes ◽  
Edita Kolarova
Keyword(s):  
Differential Equations ◽  
Transmission Line ◽  
Stochastic Differential Equations ◽  
Random Effects ◽  
Transmission Line Models

scholarly journals Estimation of parameters in stochastic differential equations with two random effects

2016 ◽  
Vol 5 (2) ◽  
pp. 97
Author(s):  
Mohammed Alsukaini ◽  
Walaa Alkreemawi ◽  
Xiang-Jun Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Effects ◽  
Posterior Distribution ◽  
Diffusion Coefficients ◽  
Likelihood Function ◽  
Random Effect ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Consistency And Asymptotic Normality

<p>In this paper we investigate consistency and asymptotic normality of the posterior distribution of the parameters in the stochastic differential equations (SDE’s) with diffusion coefficients depending nonlinearly on a random variables  and  (the random effects).The distributions of the random effects  and  depends on unknown parameters which are to be estimated from the continuous observations of the independent processes . We propose the Gaussian distribution for the random effect  and the exponential distribution for the random effect    , we obtained an explicit formula for the likelihood function and find the estimators of the unknown parameters in the random effects.</p>

scholarly journals Parametric inference for stochastic differential equations with random effects in the drift coefficient

2016 ◽  
Vol 4 (2) ◽  
pp. 21
Author(s):  
Alsukaini Mohammed Sari ◽  
Wang Xiang-Jun
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Effects ◽  
Unknown Parameter ◽  
Random Effect ◽  
Maximum Likelihood Estimators ◽  
Unknown Parameters ◽  
Explicit Formulas ◽  
Likelihood Functions ◽  
Consistency And Asymptotic Normality

In this paper we focus on estimating the parameters in the stochastic differential equations (SDE’s) with drift coefficients depending linearly on a random variables  and  .The distributions of the random effects  and  are depends on unknown parameters from the continuous observations of the independent processes . When  is an unknown parameter or restrict positive constant also studied in this paper. We propose the Gaussian distribution for the random effect  and the exponential distribution for the random effect    , we obtained an explicit formulas for the likelihood functions in each case and find the maximum likelihood estimators of the unknown parameters in the random effects and for the unknown parameter    . Consistency and asymptotic normality are studied just when  is normal random effect and  is constant.

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