Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the
Stochastic Geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, the
Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications the
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build
Based on the author’s more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the model
This is a reprint of a collection of 23 essays by Good (1916-2009) on philosophical perspectives on statistical inference originally published by University of Minnesota Press in 1983. Good, a statist
Based on a highly popular, well-established course taught by the authors, Stochastic Processes: An Introduction, Second Edition discusses the modeling and analysis of random experiments using the theo
Updated to conform to MathematicaR 7.0, Introduction to Probability with MathematicaR, Second Edition continues to show students how to easily create simulations from templates and solve problems usin
This text for a one-semester, calculus-based probability course focuses on the utility of probability in solving real-world problems. It can be used with students who have a solid background in integr
This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author's philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management.
Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathemat
Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You
An accessible and engaging introduction to the study of probability and statistics Utilizing entertaining real-world examples, A Probability and Statistics Companion provides aunique, interesting, an
With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything fr
Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random num
This classic text and reference collects the many formulae and methods that can be found in the scientific literature on stochastic methods. This fourth edition has been thoroughly updated and restruc
The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related to number theory, algebra, and topology. The fi
A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the prope
Explanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software e
