IJPAM: Volume 68, No. 4 (2011)

MILSTEIN APPROXIMATION OF
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: [email protected]


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