The Existence of Smooth Densities for the Prediction, Filtering and Smoothing Problems

Abstract

Stochastic flows are used to derive martingale representation results and formulae for integration by parts in function space. In turn these, give results on the existence of densities for filtering, smoothing and, prediction problems. Stochastic flows are also used to derive minimum principles in stochastic control, and new equations for the adjoint process. Related results are also obtained for jump processes and the control of Markov chains. Martingale representation results are used to minimize expected risk. Using integration by parts reverse time representations of jump processes are obtained. These results have applications in, for example, smoothing and the Malliavin calculus.

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Document Details

Document Type
Technical Report
Publication Date
Dec 20, 1990
Accession Number
ADA233039

Entities

People

  • Robert J. Elliott

Organizations

  • University of Alberta

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Calculus
  • Computational Science
  • Differential Equations
  • Equations
  • Filtration
  • Markov Chains
  • Markov Processes
  • Mathematical Filters
  • Military Research
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Stochastic Control
  • Stochastic Processes
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space