Abstract
In this paper, we consider an identification problem for a system of partially observed linear stochastic differential equations. We present a result whereby one can determine all the system parameters including the covariance matrices of the noise processes. We formulate the original identification problem as a deterministic control problem and prove the equivalence of the two problems. The method of simulated annealing is used to develop a computational algorithm for identifying the unknown parameters from the available observation. The procedure is then illustrated by some examples.
Highlights
Over the last several years, considerable attention has been focused on an identification problem of stochastic systems governed by linear or nonlinear It6 equations [2, 3, 7, 8, 10]
In [8], Liptser and Shiryayev considered the identification problem for a class of completely observed systems governed by a stochastic differential equation of the form dX(t) h(t,X(t))adt + dW(t), t_0, (1)
In [7], Legland considered an identification problem for a more general class of systems governed by stochastic differential equations of the form dy(t) h(a,X(t))dt + dW(t), t >_ O, (2)
Summary
Over the last several years, considerable attention has been focused on an identification problem of stochastic systems governed by linear or nonlinear It6 equations [2, 3, 7, 8, 10]. In [7], Legland considered an identification problem for a more general class of systems governed by stochastic differential equations of the form dy(t) h(a,X(t))dt + dW(t), t >_ O,. In [3], Dabbous and Ahmed considered the problem of identification of drift and dispersion parameters for a general class of partially observed systems governed by the following system of It6 equations dX(t) a(t, X(t), a)dt + b(t, X(t), c)dW(t), t [0, T], X(O) Xo, dy(t) h(X(t), a)dt + ro(t y(t))dWo(t), t e [0, T], y(O) O. In this paper we consider partially observed linear problems and develop techniques for identification of all the parameters including the covariance matrices of the Wiener processes without resorting to PDE. We formulate this problem as a deterministic control problem and use a simulated annealing algorithm to estimate the unknown parameters
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