The Theory of Stochastic Processes i

This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others.

This volume deals with the theory of Markov Decision Processes (MDPs) and their applications.

This monograph surveys recent results on the use of stochastic geometry for the performance analysis of large wireless networks. It is structured in two volumes. Volume I focuses on stochastic geometry and on the evaluation of spatial averages within this context.

Authors: Itô, Kiyosi
Gives a beautiful elementary treatment of general Poisson point processes in Chapter 1, especially recommended for beginners
Shows how the notion of Poisson point processes with values in a function space of paths called excursions plays a key role in an extension problem of Markov processes in Chapter 2
Demonstrates how the general theory in Chapter 2 can answer completely the extension problem for the minimal diffusion on [0, ∞) with an exit boundary 0[/i]

This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field.

Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms.