Conditional moment generating functions for integrals and stochastic integrals

TitleConditional moment generating functions for integrals and stochastic integrals
Publication TypeJournal Article
Year of Publication2003
AuthorsCharalambous, C. D., R. J. Elliott, and V. Krishnamurthy
JournalSIAM Journal on Control and Optimization
Volume42
Pagination1578–1603
ISSN0363-0129
Abstract

In this paper we present two methods for computing filtered estimates for moments of integrals and stochastic integrals of continuous-time nonlinear systems. The first method utilizes recursive stochastic partial differential equations. The second method utilizes conditional moment generating functions. An application of these methods leads to the discovery of new classes of finite-dimensional filters. For the case of Gaussian systems the recursive computations involve integrations with respect to Gaussian densities, while the moment generating functions involve differentiations of parameter dependent ordinary stochastic differential equations. These filters can be used in Volterra or Wiener chaos expansions and the expectation-maximization algorithm. The latter yields maximum-likelihood estimates for identifying parameters in state space models.

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