Filtering systems of coupled stochastic differential equations partially observed at high frequency
Fearnhead, Paul, Papaspiliopoulos, Omiros, Roberts, Gareth O. and Stuart, A. M. (2007) Filtering systems of coupled stochastic differential equations partially observed at high frequency. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2007 (No.11).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
We consider online analysis of systems of stochastic differential equations (SDEs),
from high-frequency data. The class of SDEs we focus on have constant volatility and
a drift function that is of gradient form. For these models we present a particle filter
that is able to analyse the full data, but whose computational cost does not increase
as the frequency of the data increases. The method is based on novel extensions
of the exact algorithm for simulation and inference of diffusions, and the filters do
not need to introduce any approximations through time-discretisation of the process.
The new methods have important practical and theoretical advantages over existing
filtering methods for this problem. We demonstrate our method on a number of
simulated examples, including two motivated by molecular dynamics.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Stochastic differential equations, Filters (Mathematics)|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||29|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
Ait-Sahalia, Y., Mykland, P. and Zhang, L. (2005a). How often to sample a continuous-
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