A Modern Approach to Probability Theory [Hardcover]

Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applicationsBayesian statistics, financial mathematics, information theory, tomography, and signal processingappear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

Overview This book is intended as a textbook in probability for graduate students in math? ematics and related areas such as statistics, economics, physics, and operations research. Probability theory is a 'difficult' but productive marriage of mathemat? ical abstraction and everyday intuition, and we have attempted to exhibit this fact. Thus we may appear at times to be obsessively careful in our presentation of the material, but our experience has shown that many students find them? selves quite handicapped because they have never properly come to grips with the subtleties of the definitions and mathematical structures that form the foun? dation of the field. Also, students may find many of the examples and problems to be computationally challenging, but it is our belief that one of the fascinat? ing aspects of prob ability theory is its ability to say something concrete about the world around us, and we have done our best to coax the student into doing explicit calculations, often in the context of apparently elementary models. The practical applications of probability theory to various scientific fields are far-reaching, and a specialized treatment would be required to do justice to the interrelations belsP