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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximum likelihood estimation in Skorohod stochastic differential equations


Author: Jaya P. N. Bishwal
Journal: Proc. Amer. Math. Soc. 138 (2010), 1471-1478
MSC (2010): Primary 62F12, 62M05; Secondary 60F05, 60H05, 60H10
Published electronically: November 12, 2009
MathSciNet review: 2578541
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Abstract: Consistency and limit distribution of the maximum likelihood estimator of a parameter in the drift coefficient of an anticipative Skorohod stochastic differential equation satisfying a boundary condition are obtained based on $ n$ independent trajectories of the corresponding Skorohod diffusion inside a time interval $ [0, T]$ as $ n \rightarrow \infty$. The results are illustrated for the anticipative Ornstein-Uhlenbeck process.


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Additional Information

Jaya P. N. Bishwal
Affiliation: Department of Mathematics and Statistics, University of North Carolina at Charlotte, 376 Fretwell Building, 9201 University City Boulevard, Charlotte, North Carolina 28223-0001
Email: J.Bishwal@uncc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10113-2
PII: S 0002-9939(09)10113-2
Keywords: Skorohod stochastic differential equations, Skorohod integral, anticipative Girsanov transformation, maximum likelihood estimator, consistency, limit distribution, Carleman-Fredholm determinant.
Received by editor(s): August 15, 2008
Received by editor(s) in revised form: May 15, 2009
Published electronically: November 12, 2009
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2009 American Mathematical Society