Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.

Applied Probability and Stochastic Processes, Second Edition presents a self-contained introduction to elementary probability theory and stochastic processes with a special emphasis on their applications in science, engineering, finance, computer science, and operations research. It covers the theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates applications through the analysis of numerous practical examples. The author draws on his 50 years of experience in the field to give your students a better understanding of probability theory and stochastic processes and enable them to use stochastic modeling in their work. New to the Second Edition Completely rewritten part on probability theory—now more than double in size New sections on time series analysis, random walks, branching processes, and spectral analysis of stationary stochastic processes Comprehensive numerical discussions of examples, which replace the more theoretically challenging sections Additional examples, exercises, and figures Presenting the material in a student-friendly, application-oriented manner, this non-measure theoretic text only assumes a mathematical maturity that applied science students acquire during their undergraduate studies in mathematics. Many exercises allow students to assess their understanding of the topics. In addition, the book occasionally describes connections between probabilistic concepts and corresponding statistical approaches to facilitate comprehension. Some important proofs and challenging examples and exercises are also included for more theoretically interested readers.

The Athens Conference on Applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes. Volume I includes papers on applied probability in Honor of J.M. Gani. The topics include probability and probabilistic methods in recursive algorithms and stochastic models, Markov and other stochastic models such as Markov chains, branching processes and semi-Markov systems, biomathematical and genetic models, epidemilogical models including S-I-R (Susceptible-Infective-Removal), household and AIDS epidemics, financial models for option pricing and optimization problems, random walks, queues and their waiting times, and spatial models for earthquakes and inference on spatial models.

This book is devoted to Professor Jürgen Lehn, who passed away on September 29, 2008, at the age of 67. It contains invited papers that were presented at the Wo- shop on Recent Developments in Applied Probability and Statistics Dedicated to the Memory of Professor Jürgen Lehn, Middle East Technical University (METU), Ankara, April 23–24, 2009, which was jointly organized by the Technische Univ- sität Darmstadt (TUD) and METU. The papers present surveys on recent devel- ments in the area of applied probability and statistics. In addition, papers from the Panel Discussion: Impact of Mathematics in Science, Technology and Economics are included. Jürgen Lehn was born on the 28th of April, 1941 in Karlsruhe. From 1961 to 1968 he studied mathematics in Freiburg and Karlsruhe, and obtained a Diploma in Mathematics from the University of Karlsruhe in 1968. He obtained his Ph.D. at the University of Regensburg in 1972, and his Habilitation at the University of Karlsruhe in 1978. Later in 1978, he became a C3 level professor of Mathematical Statistics at the University of Marburg. In 1980 he was promoted to a C4 level professorship in mathematics at the TUD where he was a researcher until his death.

A graduate text on theory and methods using applied probability techniques for scheduling service, manufacturing, and information networks.

Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.