Rabi Bhattacharya's Books

Asymptotic Statistics

By: Manfred Denker,Rabi Bhattacharya

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These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 {sect}1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx)

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121

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Birkhäuser

Published Date

ISBN 10

3034892543

ISBN 13

9783034892544

Continuous Parameter Markov Processes and Stochastic Differential Equations

By: Rabi Bhattacharya,Edward C. Waymire

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Continuous Parameter Markov Processes and Stochastic Differential Equations

By: Rabi Bhattacharya,Edward C. Waymire

This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples. After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media.

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502

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Springer Nature

Published Date

ISBN 10

3031332962

ISBN 13

9783031332968

Stationary Processes and Discrete Parameter Markov Processes

By: Rabi Bhattacharya,Edward C. Waymire

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Stationary Processes and Discrete Parameter Markov Processes

By: Rabi Bhattacharya,Edward C. Waymire

This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff’s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth–death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.

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449

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Springer Nature

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ISBN 10

3031009436

ISBN 13

9783031009433

Basin Evolution and Petroleum Prospectivity of the Continental Margins of India

By: Rabi Bastia,M. Radhakrishna

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Basin Evolution and Petroleum Prospectivity of the Continental Margins of India

By: Rabi Bastia,M. Radhakrishna

During the past 10 years, the Oil industry in India has seen a tremendous rise in exploration activity with several major E&P companies generating vast amount of new geological and geophysical data. The availability of such integrated data sets (gravity, magnetic, seismic, drilled wells), especially in the deep offshore basins, has led the authors to revisit earlier concepts and models in order to redefine the tectonic framework of major offshore basins along the Indian continental margins. The book covers the stratigraphic evolution, play types and the classification of major offshore basins both in shallow and deepwater environments. - Incorporation of latest dataset (specially the seismic, gravity and magnetic) - Analogy of global offshore basins with India - Sedimentation and depositional history of Bengal fan and Indus fan - Redefinition of major tectonic framework of the margins - Exceleent high quality graphics that include: seismic sections, gravity-magnetic maps, conceptual geological models and new revised tectonic elements

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431

Publisher

Newnes

Published Date

ISBN 10

0444536051

ISBN 13

9780444536051

Normal Approximation and Asymptotic Expansions

By: Rabi N. Bhattacharya,R. Ranga Rao

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Normal Approximation and Asymptotic Expansions

By: Rabi N. Bhattacharya,R. Ranga Rao

-Fourier analysis, --

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333

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SIAM

Published Date

ISBN 10

089871897X

ISBN 13

9780898718973

Stochastic Processes with Applications

By: Rabi N. Bhattacharya,Edward C. Waymire

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Stochastic Processes with Applications

By: Rabi N. Bhattacharya,Edward C. Waymire

This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes. The book features very broad coverage of the most applicable aspects of stochastic processes, including sufficient material for self-contained courses on random walks in one and multiple dimensions; Markov chains in discrete and continuous times, including birth-death processes; Brownian motion and diffusions; stochastic optimization; and stochastic differential equations. This book is for graduate students in mathematics, statistics, science and engineering, and it may also be used as a reference by professionals in diverse fields whose work involves the application of probability.

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Page Count

726

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SIAM

Published Date

ISBN 10

0898716896

ISBN 13

9780898716894

A Course in Mathematical Statistics and Large Sample Theory

By: Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru

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A Course in Mathematical Statistics and Large Sample Theory

By: Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru

This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

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Page Count

386

Publisher

Springer

Published Date

ISBN 10

1493940325

ISBN 13

9781493940325

Nonparametric Inference on Manifolds

With Applications to Shape Spaces

By: Abhishek Bhattacharya,Rabi Bhattacharya

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Nonparametric Inference on Manifolds

With Applications to Shape Spaces

By: Abhishek Bhattacharya,Rabi Bhattacharya

Ideal for statisticians, this book will also interest probabilists, mathematicians, computer scientists, and morphometricians with mathematical training. It presents a systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important applications in medical diagnostics, image analysis and machine vision.

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Page Count

252

Publisher

Cambridge University Press

Published Date

ISBN 10

1107019583

ISBN 13

9781107019584

Source-Synchronous Networks-On-Chip

Circuit and Architectural Interconnect Modeling

By: Ayan Mandal,Sunil P. Khatri,Rabi Mahapatra

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Source-Synchronous Networks-On-Chip

Circuit and Architectural Interconnect Modeling

By: Ayan Mandal,Sunil P. Khatri,Rabi Mahapatra

This book describes novel methods for network-on-chip (NoC) design, using source-synchronous high-speed resonant clocks. The authors discuss NoCs from the bottom up, providing circuit level details, before providing architectural simulations. As a result, readers will get a complete picture of how a NoC can be designed and optimized. Using the methods described in this book, readers are enabled to design NoCs that are 5X better than existing approaches in terms of latency and throughput and can also sustain a significantly greater amount of traffic.

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151

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Springer Science & Business Media

Published Date

ISBN 10

1461494052

ISBN 13

9781461494058

A Basic Course in Probability Theory

By: Rabi Bhattacharya,Edward C. Waymire

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A Basic Course in Probability Theory

By: Rabi Bhattacharya,Edward C. Waymire

Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path.

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217

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Springer Science & Business Media

Published Date

ISBN 10

0387719385

ISBN 13

9780387719382

Asymptotic Statistics

By: Manfred Denker,Rabi Bhattacharya

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Asymptotic Statistics

By: Manfred Denker,Rabi Bhattacharya

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121

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Birkhäuser

Published Date

ISBN 10

3034892543

ISBN 13

9783034892544

Random Dynamical Systems

Theory and Applications

By: Rabi Bhattacharya,Mukul Majumdar

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Random Dynamical Systems

Theory and Applications

By: Rabi Bhattacharya,Mukul Majumdar

This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.

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Cambridge University Press

Published Date

ISBN 10

1139461621

ISBN 13

9781139461627

Random Walk, Brownian Motion, and Martingales

By: Rabi Bhattacharya,Edward C. Waymire

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Random Walk, Brownian Motion, and Martingales

By: Rabi Bhattacharya,Edward C. Waymire

This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.

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Page Count

396

Publisher

Springer Nature

Published Date

ISBN 10

303078939X

ISBN 13

9783030789398

Normal Approximation and Asymptotic Expansions

By: Rabi N. Bhattacharya,R. Ranga Rao

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Normal Approximation and Asymptotic Expansions

By: Rabi N. Bhattacharya,R. Ranga Rao

-Fourier analysis, --

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Page Count

333

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SIAM

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ISBN 10

089871897X

ISBN 13

9780898718973

Book's by Rabi Bhattacharya

Asymptotic Statistics

Asymptotic Statistics

Continuous Parameter Markov Processes and Stochastic Differential Equations

Continuous Parameter Markov Processes and Stochastic Differential Equations

Stationary Processes and Discrete Parameter Markov Processes

Stationary Processes and Discrete Parameter Markov Processes

Basin Evolution and Petroleum Prospectivity of the Continental Margins of India

Basin Evolution and Petroleum Prospectivity of the Continental Margins of India

Normal Approximation and Asymptotic Expansions

Normal Approximation and Asymptotic Expansions

Stochastic Processes with Applications

Stochastic Processes with Applications

A Course in Mathematical Statistics and Large Sample Theory

A Course in Mathematical Statistics and Large Sample Theory

Nonparametric Inference on Manifolds

Nonparametric Inference on Manifolds

Source-Synchronous Networks-On-Chip

Source-Synchronous Networks-On-Chip

A Basic Course in Probability Theory

A Basic Course in Probability Theory

Asymptotic Statistics

Asymptotic Statistics

Random Dynamical Systems

Random Dynamical Systems

Random Walk, Brownian Motion, and Martingales

Random Walk, Brownian Motion, and Martingales

Normal Approximation and Asymptotic Expansions

Normal Approximation and Asymptotic Expansions

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