![](/images/graphics-bg.png)
On Local Linear Approximations to Diffusion Processes
Joint Authors
Duan, X. L.
Qian, Z. M.
Zheng, W. A.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-09-27
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
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 and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth.
Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) 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.
American Psychological Association (APA)
Duan, X. L.& Qian, Z. M.& Zheng, W. A.. 2011. On Local Linear Approximations to Diffusion Processes. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-507054
Modern Language Association (MLA)
Duan, X. L.…[et al.]. On Local Linear Approximations to Diffusion Processes. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-26.
https://search.emarefa.net/detail/BIM-507054
American Medical Association (AMA)
Duan, X. L.& Qian, Z. M.& Zheng, W. A.. On Local Linear Approximations to Diffusion Processes. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-26.
https://search.emarefa.net/detail/BIM-507054
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507054