Gopinath Kallianpur's Books

Stochastic Analysis and Diffusion Processes

By: Gopinath Kallianpur,P Sundar

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Stochastic Analysis and Diffusion Processes

By: Gopinath Kallianpur,P Sundar

Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.

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Page Count

368

Publisher

OUP Oxford

Published Date

ISBN 10

0191004529

ISBN 13

9780191004520

Introduction to Option Pricing Theory

By: Gopinath Kallianpur,Rajeeva L. Karandikar

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Introduction to Option Pricing Theory

By: Gopinath Kallianpur,Rajeeva L. Karandikar

Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

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Page Count

266

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461205115

ISBN 13

9781461205111

White Noise Theory of Prediction, Filtering and Smoothing

By: Gopinath Kallianpur,Rajeeva L. Karandikar

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White Noise Theory of Prediction, Filtering and Smoothing

By: Gopinath Kallianpur,Rajeeva L. Karandikar

Based on the author’s own research, this book rigorously and systematically develops the theory of Gaussian white noise measures on Hilbert spaces to provide a comprehensive account of nonlinear filtering theory. Covers Markov processes, cylinder and quasi-cylinder probabilities and conditional expectation as well as predictio0n and smoothing and the varied processes used in filtering. Especially useful for electronic engineers and mathematical statisticians for explaining the systematic use of finely additive white noise theory leading to a more simplified and direct presentation.

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Page Count

624

Publisher

CRC Press

Published Date

ISBN 10

2881246850

ISBN 13

9782881246852

Stochastic Analysis and Diffusion Processes

By: Gopinath Kallianpur,P Sundar

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Stochastic Analysis and Diffusion Processes

By: Gopinath Kallianpur,P Sundar

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Page Count

365

Publisher

OUP Oxford

Published Date

ISBN 10

0191631442

ISBN 13

9780191631443

Book's by Gopinath Kallianpur

Stochastic Analysis and Diffusion Processes

Stochastic Analysis and Diffusion Processes

Introduction to Option Pricing Theory

Introduction to Option Pricing Theory

White Noise Theory of Prediction, Filtering and Smoothing

White Noise Theory of Prediction, Filtering and Smoothing

Stochastic Analysis and Diffusion Processes

Stochastic Analysis and Diffusion Processes

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