Titlebook: Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems; Harold J. Kushner Book 1990 Birkhäuser Boston

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The Nonlinear Filtering Problem,em of control approximations. In this chapter, we will be concerned with approximations for the nonlinear filtering problem. Suppose that we observe the noise corrupted data .(•) defined by ., where .(•) is a standard vector-valued Wiener process. Owing to the complexity and high dimension of the or

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Weak Convergence: The Perturbed Test Function Method,white noise driven” Itô equations which were used there. For the singular perturbation problem of Chapter 4, with model (4.1.1), (4.1.2) with control .(·), the martingale method which was used to characterize the limit process can be roughly described as follows (see Theorem 4.1.2): We apply the dif

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Stability Theory,tability. Of course, if the state spaces are bounded, then the cited as­sumptions are automatically satisfied. The deterministic specialization of the above cited tightness requirements is that the trajectories of interest (those of .(ּ) and/or x.(ּ)) be bounded on the time interval of interest. To

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