Two-Scale Stochastic Systems Asymptotic Analysis and Control [Hardcover]

0 Warm-up.- 1 Toolbox: Moment Bounds for Solutions of Stable SDEs.- 2 The Tikhonov Theory for SDEs.- 3 Large Deviations.- 4 Uniform Expansions for Two-Scale Systems.- 5 Two-Scale Optimal Control Problems.- 6 Applications.- A.1 Basic Facts About SDEs.- A.1.1 Existence and Uniqueness of Strong Solutions for SDEs with Random Coefficients.- A.1.2 Existence and Uniqueness with a Lyapunov Function.- A.1.3 Moment Bounds for Linear SDEs.- A.1.4 The Novikov Condition.- A.2 Exponential Bounds for Fundamental Matrices.- A.2.1 Uniform Bound in the Time-Homogeneous Case.- A.2.2 Nonhomogeneous Case.- A.2.3 Models with Singular Perturbations.- A.3 Total Variation Distance and Hellinger Processes.- A.3.1 Total Variation Distance and Hellinger Integrals.- A.3.2 The Hellinger Processes.- A.3.3 Example: Diffusion-Type Processes.- A.4 Hausdorff Metric.- A.5 Measurable Selection.- A.5.1 Aumann Theorem.- A.5.2 Filippov Implicit Function Lemma.- A.5.3 Measurable Version of the Carath?odory Theorem.- A.6.1 Notations and Preliminaries.- A.6.2 Integration of Stochastic Kernels.- A.6.3 Distributions of Integrals.- A.6.4 Compactness of the Limit of Attainability Sets.- A.6.5 Supports of Conditional Distributions.- A.7 The Koml?s Theorem.- Historical Notes.- References.

From the reviews:

The book presents Tikhonov theorems for stochastic systems with two time scales when a parameter decreases to zero. & The topic of the book is relevant for the research areas of stochastics and of control and system theory. & The strength of the book is in the analysis of Tikhonov theorems & . The text is very well structured, runs very smooth, and the exposition allows detailed scrutiny of all proofs. The book is expected to become a basic reference on two-scale stochastic systems. (J. H. van Schuppen, Nieuw Archief voor Wiskunde, Vol. 6 (2), 2005)

This research monograph needs to be placed on your shelves & . The monograph is organized by sevenlcC