Asymptotic Bayesian Estimation of a First Order Equation with Small Diffusion

In this paper a finite-dimensional diffusion is observed in the presence of an additive Brownian motion. A large deviations result is obtained for the conditional probability distribution of the diffusion given the observations as the noise variances go to zero.

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Bibliographic Details
Published in:The Annals of probability 1984-08, Vol.12 (3), p.890-902
Main Author: Hijab, Omar
Format: Article
Language:English
Subjects:
58G32
60F10
93E10
Bayesian estimation
Brownian motion
Differential equations
diffusion
Exact sciences and technology
Hijabs
Large deviations
Limit theorems
Mathematics
Probability and statistics
Probability distributions
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Vector fields
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Description
Summary:In this paper a finite-dimensional diffusion is observed in the presence of an additive Brownian motion. A large deviations result is obtained for the conditional probability distribution of the diffusion given the observations as the noise variances go to zero.
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1176993238