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Probability Theory : a foundational course / R P Pakshirajan

By: Pakshirajan, R. PContributor(s): Pakshirajan, R. PMaterial type: Text

TextPublisher number: :Variety Books Publishers & Distributors | :B-10 Street No 2 West Vinod Nagar Delhi 110092 Series: Texts and readings in mathematics, 63Publication details: New Delhi, India : Hindustan Book Agency, 2013Description: xv, 560 pages 24cmISBN: 9789380250441Subject(s): Mathematics | Probabilities and applied mathematics | ProbabilitiesDDC classification: 519.2 PAK

Contents:

Probability measures in product spaces -- Weak convergence of probability measures -- Characteristic functions -- Independence -- The central limit theorem and its ramifications -- The law of the iterated logarithm -- Discrete time Markov chains.

Summary: This book shares the dictum of J.L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject

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Holdings
Item type	Current library	Call number	Status	Notes	Date due	Barcode	Item holds
Mathematics Departmental Library	SNU LIBRARY	519.2 PAK (Browse shelf(Opens below))	Available	FPDA Grant		M249

Total holds: 0

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Probability measures in product spaces --
Weak convergence of probability measures --
Characteristic functions --
Independence --
The central limit theorem and its ramifications --
The law of the iterated logarithm --
Discrete time Markov chains.

This book shares the dictum of J.L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject

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