Optimal linear nonstationary filtering

  • R. S. Liptser
  • A. N. Shiryayev
Part of the Applications of Mathematics book series (SMAP, volume 5)


On the probability space (Ω,,P) with a distinguished family of the σ-algebras ( t ),tT, we shall consider the two-dimensional Gaussian random process (θ t , t),0 ≤ tT,satisfying the stochastic differential equations
$$ d{\theta _t} = a(t){\theta _t}dt + b(t)d{W_1}(t) $$
$$ d{\xi _t} = A(t){\theta _t}dt + B(t)d{W_2}(t) $$
where W 1 =(W 1(t) t )and W 2 =(W 2(t) t ) are two independent Wiener processes and θ 0,ξ 0, are 0-measurable.


Conditional Expectation Wiener Process Multidimensional Case Gaussian Random Process Integrable Martingale 
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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • R. S. Liptser
    • 1
  • A. N. Shiryayev
    • 2
  1. 1.Institute for Problems of Control TheoryMoscowUSSR
  2. 2.Institute of Control SciencesMoscowUSSR

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