A note on the existence of a closed form conditional transition density for the Milstein scheme
AbstractThis paper is concerned with the estimation of stochastic differential equations when only discrete observations are available. It primarily focuses on deriving a closed form solution for the one-step ahead conditional transition density using the Milstein scheme. This higher order Taylor approximation enables us to obtain an order of improvement in accuracy in estimating the parameters in a non-linear diffusion, as compared to use of the Euler-Maruyama discretization scheme. Examples using simulated data are presented. The method can easily be extended to the situation where auxiliary points are introduced between the observed values. The Milstein scheme can be used to obtain the approximate transition density as in a Pedersen (1995) type of simulated likelihood method or within an MCMC method as propose din Elerian, Chib and Shephard (1998).
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Bibliographic InfoPaper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 1998-W18.
Date of creation: 01 Oct 1998
Date of revision:
Bayes estimation; nonlinear diffusion; Euler-Maruyama approximation; Maximum Likelihood; Markov chain Monte Carlo; Metropolis Hastings algorithm; Milstein scheme; Simulation; Stochastic Differential Equation.;
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