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The Filtering Problem

  • Bernt Øksendal
Chapter
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Part of the Universitext book series (UTX)

Abstract

Problem 3 in the introduction is a special case of the following general filtering problem:

Suppose the state Xt ∈ ℝn at a time t of a system is given by a stochastic differential equation
$$\frac{{dX_t }} {{dt}} = b\left( {t,X_t } \right) + \sigma \left( {t,X_t } \right)W_t ,$$
(6.1)
where b: ℝn → ℝn σ: ℝn+1 → ℝn×p satisfy conditions (5.14), (5.15) and Wt is p-dimensional white noise.

Keywords

Brownian Motion Stochastic Differential Equation Innovation Process Riccati Equation Noisy Observation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Bernt Øksendal
    • 1
  1. 1.Department of MathematicsUniversity of OsloBlindern, Oslo 3Norway

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