Probability & Statistics

Essential Textbook Basic Probability

What Every Math Student Should Know (2nd Edition)

by Henk Tijms (Vrije University, The Netherlands) The second edition represents an ongoing effort to make probability accessible to students in a wide range of fields such as mathematics, statistics and data science, engineering, computer science, and business analytics. While retaining its focus on basic probability, including Bayesian probability and the interface between probability and computer simulation, this edition’s significant revisions are as follows: • Many extra motivational examples and problems • New material on Bayesian probability, including two famous court cases • New sections on real-world applications of the Poisson distribution • New sections on generating functions and the bivariate normal density • New chapter on Markov chains, including Markov chain Monte Carlo simulation Readership: Undergraduate students in fields such as mathematics, statistics and data science, engineering, computer science and business analytics. Graduate students in natural and social sciences. Students taking a first course in probability, or a course on probability for statistics and data science.

184pp Aug 2021 978-981-123-851-2(pbk) US$34 £30 978-981-123-749-2 US$58 £50

Inequalities in Analysis and Probability

(3rd Edition)

by Odile Pons (National Institute for Agronomical Research, France) The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes. In this third edition, the inequalities for martingales are presented in two chapters for discrete and timecontinuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes. Readership: Advanced undergraduate and graduate students as well as researchers in probability and integration theory. The book may be used for courses in analysis and integration theory for undergraduate students.

370pp 978-981-123-134-6 Nov 2021 US$128 £115

World Scientific Series on Probability Theory and Its Applications - Vol 2

Introduction to Stochastic Processes

by Mu-Fa Chen (Beijing Normal University, China) & Yong-Hua Mao (Beijing Normal University, China) The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying. This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. Readership: Advanced undergraduate and graduate students.

244pp 978-981-4740-30-2

An Unbounded Experience in Random Walks with Applications

by Michael F Shlesinger This volume comprises the author’s account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lévy’s work via Mandelbrot’s Lévy flights which are featured uniquely as Weierstrass and Riemann random walks. Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green’s functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.

Readership: Graduate students in the physical sciences and mathematics, and researchers in stochastic processes. Scientists and teachers interested in the history of probability and the development of random walks during the fractal and chaos revolutions.

216pp 978-981-123-280-0 Jul 2021 US$78 £70

Series on Multivariate Analysis - Vol 13 Hilbert and Banach SpaceValued Stochastic Processes

by Yûichirô Kakihara (California State University, San Bernardino, USA) This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinitedimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon – Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes. Readership: Graduate students in mathematics, probabilists, statisticians, functional analysts, communication engineers and physicists.

540pp 978-981-121-174-4 Aug 2021 US$168 £150

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World Scientific Series on Probability Theory and Its Applications - Volume 3

Introduction to Probability Theory

A First Course on the Measure-Theoretic Approach

by Nima Moshayedi (University of Zurich, Switzerland & University of California, Berkeley, USA) This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.

Key Features:

• The book was created out of a given lecture, so it addresses the most common problems of understanding for students and it aims to explain these things more carefully • The topics are intended to be well-separated • The sections are covered with minor exercises, such as simple proofs, to train the student’s understanding Readership: Undergraduate students in mathematics and physics majors. Undergraduate students in economy, finance, engineering or any other subject that includes probability theory in the curriculum.

175pp Apr 2022 978-981-124-674-6 US$68 £60

Chance, Logic and Intuition

An Introduction to the Counter-Intuitive Logic of Chance

by Steven Tijms “This charming book discusses some of the most striking misconceptions about randomness, from antiquity to the current Covid-19 crisis.” Ted Hill, Professor Emeritus of

Mathematics, Georgia Institute of Technology

“I am not aware of any previous attempt to write an introduction to probability with such a varied and detailed tour of the lives of its founding fathers, along with modern-day anecdotes.”

John Haigh, Emeritus Reader in Statistics, University of Sussex, Author of Taking Chances

“There were parts of the history section covering aspects that I’ve rarely seen before in a popular mathematics text ... this is a genuinely useful addition to the popular maths coverage of probability.” Popular Science Books Readership:General public; STEM students in mathematics; college and high school math teachers; various academics interested in probability theory.

256pp Mar 2021 978-981-124-783-5(pbk) US$34 £30 978-981-122-918-3 US$68 £60

Probability Theory

An Elementary Course

by Zhengyan Lin (Zhejiang University, China), Zhonggen Su (Zhejiang University, China) & Lixin Zhang (Zhejiang University, China) This volume introduces various concepts that quantitatively describe random phenomena, including probability, random variables, distribution functions, density functions, mathematical expectations, variances, moments, and characteristic functions. It finishes off by presenting probability limit theory, including various convergences. Throughout the volume, great importance is attached to the elaboration of probability thoughts. For this reason, some practical examples to illustrate the introduced concept are always used. This volume contains a large number of problems of varying levels for the reader with the purpose to review, consolidate, deepen and expand their knowledge. Readership: Undergraduate and graduate students, and researchers interested in probability theory.

350pp Jul 2022 978-981-120-019-9 US$98 £85

Harmonizable Theory

by M M Rao (University of California, Riverside, USA)

The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy’s Brownian motion, a probabilistic proof of the longstanding Riemann’s hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér – Karhunen classes, as well as bistochastic operators with some statistical applications. The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications.

Readership: Graduate students and researchers in probability and statistics interested in stochastic processes and harmonizable processes. Electrical-communication engineers as well as other applied professionals in these fields.

340pp 978-981-121-365-6 Oct 2020 US$128 £115

Probability

Theory, Examples, Problems, Simulations

by Hannelore Lisei (Babeş-Bolyai University, Romania), Wilfried Grecksch (Martin-Luther-University HalleWittenberg, Germany) & Mihai Iancu (Babeş-Bolyai University, Romania)

A key pedagogical feature of the textbook is the accessible approach to probability concepts through examples with explanations and problems with solutions. The reader is encouraged to simulate in Matlab random experiments and to explore the theoretical aspects of the probabilistic models behind the studied experiments. By this appropriate balance between simulations and rigorous mathematical approach, the reader can experience the excitement of comprehending basic concepts and can develop the intuitive thinking in solving problems. The current textbook does not contain proofs for the stated theorems, but corresponding references are given.

Readership: Undergraduate and graduate students, professionals and researchers in mathematics, natural sciences, engineering and computer science areas.

364pp Feb 2020 978-981-120-719-8(pbk) US$58 £50 978-981-120-573-6 US$108 £95

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