Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

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Focusing on the approximation and perturbation of random processes, this book explores their applications in stochastic control systems and nonlinear filters. It introduces innovative mathematical methods from weak convergence theory, offering powerful techniques for deriving limit theorems across various problems. The author, building on a long-standing interest in stochastic process approximation, highlights the relevance of these methods in control and communication theory while also suggesting their applicability in broader contexts. Key processes include solutions to Ito differential equations influenced by various types of noise.