PARAMETER ESTIMATION FOR A CLASS OF DIFFUSION PROCESS FROM DISCRETE OBSERVATION

Abstract

This paper is concerned with the parameter estimation problem for a class of diffusion process with drift coefficient \(αX_{t}^{2γ−1}\) and diffusion coefficient \(σX_{t}^{γ}\) from discrete observation.  Euler-Maruyama scheme and iterative method are used to get the joint conditional probability density function.  The maximum likelihood approach is applied for obtaining the parameter estimators and the explicit expressions of the error of estimation are given.  The strong consistency of the estimators and asymptotic normality of the error of estimation are proved by using the law of large numbers for martingales, the strong law of large numbers and central-limit theorem.  Hypothesis testing is made to verify the effectiveness of the estimation method used in this paper.