On local linear approximations to diffusion processes
type: Item
instance of: scholarly article
title: On local linear approximations to diffusion processes
zbMATH Open document ID: 1278.60119
DOI: 10.1155/2011/906846
author: Juan-Miguel Gracia
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-10-26T00:00:00Z
review text: Summary: Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books of Kutoyants (2004; Zbl 1038.62073), Liptser and Shiryayev (1977; Zbl 0364.60004), Kushner and Dupuis (2001; Zbl 0968.93005), and Prakasa Rao (1999; Zbl 0952.62077), and also the recent works by Aït-Sahalia (1999; Zbl 1013.91505), and P. A. Mykland (2004; Zbl 1062.62155), (2002; Zbl 1104.62323), and so forth. Shoji and Ozaki (1998; Zbl 0912.60078) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 91G80
zbMATH DE Number: 5964016
Wikidata QID: Q58687980
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/906846
OpenAlex ID: W2063184277
cites work: On conditional diffusion processes
cites work: Smooth Transition Densities for One-Dimensional Diffusions
cites work: Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach
cites work: Estimators of diffusions with randomly spaced discrete observations: a general theory
cites work: Estimation for nonlinear stochastic differential equations by a local linearization method1
cites work: Q4947392
cites work: A representation formula for transition probability densities of diffusions and applications
cites work: Approximate maximum likelihood estimation for diffusion processes from discrete observations
cites work: Q4039796
cites work: Long-time behaviour of heat flow: Global estimates and exact asymptotics
DBLP publication ID: journals/ijmmsc/DuanQZ11
description: scientific article; zbMATH DE number 5964016