IJPAM: Volume 68, No. 4 (2011)
MILSTEIN APPROXIMATION OF
POSTERIOR DENSITY FOR DIFFUSIONS
POSTERIOR DENSITY FOR DIFFUSIONS
Jaya P.N. Bishwal
Department of Mathematics and Statistics
University of North Carolina at Charlotte
Charlotte, NC 28223-0001, USA
e-mail: J.Bishwal@uncc.edu
Department of Mathematics and Statistics
University of North Carolina at Charlotte
Charlotte, NC 28223-0001, USA
e-mail: J.Bishwal@uncc.edu
Abstract. We adopt the second order weak Milstein simulation scheme for estimating the true posterior density of diffusions and obtain the rate of weak convergence. We also obtain the Bernstein-von Mises Theorem concerning the convergence of the simulated posterior distribution to normal distribution and asymptotic normality of the Bayes estimator for smooth prior and loss functions.
Received: January 28, 2011
AMS Subject Classification: 60F05, 60F10, 60H05, 62M05, 62F12
Key Words and Phrases: diffusion processes, simulation, Milstein scheme, posterior distribution, Bernstein-von Mises Theorem
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 4
