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.

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>

On effects of discretization on estimators of drift parameters for diffusion processes

1996 ◽  
Vol 33 (04) ◽  
pp. 1061-1076 ◽  
Author(s):  
P. E. Kloeden ◽  
E. Platen ◽  
H. Schurz ◽  
M. Sørensen
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Diffusion Processes ◽  
Maximum Likelihood Estimators ◽  
Statistical Properties ◽  
Stochastic Integrals

In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

scholarly journals Maximum likelihood Estimation for Stochastic Differential Equations with two Random Effects in the Diffusion Coefficient

2016 ◽  
Vol 11 (10) ◽  
pp. 5697-5704
Author(s):  
Mohammed Sari Alsukaini ◽  
Alkreemawi khazaal Walaa ◽  
Wang Xiang Jun
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Random Effects ◽  
Diffusion Coefficients ◽  
Likelihood Function ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Unknown Parameters ◽  
Consistency And Asymptotic Normality

We study n independent stochastic processes(xi (t),tiЄ[o,t1 ],i=1,......n) defined by a stochastic differential equation with diffusion coefficients depending nonlinearly on a random variables  and  (the random effects).The distributions of the random effects Ñ„i,and,μi and  depends on unknown parameters which are to be estimated from the continuous observations of the processes xi (t) . When the distributions of the random effects Ñ„ ,μ, are Gaussian and exponential respectively, we obtained an explicit formula for the likelihood function and the asymptotic properties (consistency and asymptotic normality) of the maximum likelihood estimator (MLE) are derived when  tend to infinity.

Sign in / Sign up

Export Citation Format

Share Document