Low-Noise Analysis of Zakai’s Equation

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Abstract

Zakai’s equation is a stochastic linear parabolic initial value problem that except for the linear case, has a closed-form solution only in exceptional and not very useful cases [165]. To understand the difficulties in applying the Zakai equation to the filtering problem, we consider again the simplified one-dimensional filtering problem (3.22), (3.23), 4.1.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages107-145
Number of pages39
DOIs
StatePublished - 2012

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume180
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Conditional Moment
  • Extended Kalman Filter
  • Optimal Filter
  • Riccati Equation
  • Stochastic Differential Equation

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