The subject of this book is the problem of controlling or stabilizing a system of differential equations in the presence of random disturbances. The book is divided into five chapters. Overall the book may be grouped into two sections. The first section includes chapters 1 and 2 and it is a quick course on basic linear system theory which is the material necessary to solve the problem of stabilization and optimal control of linear systems. Only the deterministic case is considered here. The second part of the book, Chapters 3, 4 and 5, is of a more advanced nature. Chapter 3 reviews the basic probability theory needed and, in particular, the construction of the stochastic integral, the Girsanov formula. Chapter 4 deals with a relevant class of filtering problems; also the problem of Shannon information is discussed here. Chapter 5 combines the results of Chapters 2 and 4 in an analysis of the adaptive linear quadratic regulator control problem. (Zentralblatt)

bibliogr. and index