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

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Stability Theory,prove that boundedness in particular cases for the deterministic problem, some form of Liapunov function method is usually used. Stochastic “Liapunov function methods” are also very useful (if not indispensible at this time) to prove the required tightness for the stochastic problems, and we will discuss several approaches in this chapter.
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Parametric Singularities,for some constant σ. > 0. It will be seen in Section 1 that . (.) is a “wide band noise” process which converges to white noise in the sense that its integral converges to a Wiener process with a state and control dependent bias.
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Harold J. Kushneraining how solutions are found, what the system is doing, and why it operates in a certain way. The methods applied and the advice given have to be explained, s978-3-540-33587-0978-3-540-33588-7Series ISSN 0302-9743 Series E-ISSN 1611-3349
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