Statistics of Random Processes I pp 351-380 | Cite as
Optimal linear nonstationary filtering
Chapter
Abstract
On the probability space (Ω,ℱ,P) with a distinguished family of the σ-algebras (ℱ t ),t ≤ T, we shall consider the two-dimensional Gaussian random process (θ t ,ℱ t),0 ≤ t ≤ T,satisfying the stochastic differential equations where W 1 =(W 1(t)ℱ t )and W 2 =(W 2(t)ℱ t ) are two independent Wiener processes and θ 0,ξ 0, are ℱ 0-measurable.
$$
d{\theta _t} = a(t){\theta _t}dt + b(t)d{W_1}(t)
$$
(10.1)
$$
d{\xi _t} = A(t){\theta _t}dt + B(t)d{W_2}(t)
$$
(10.2)
Keywords
Conditional Expectation Wiener Process Multidimensional Case Gaussian Random Process Integrable Martingale
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© Springer Science+Business Media New York 1977