Athreya, Krishna B. 1939
Overview
Works:  47 works in 154 publications in 3 languages and 2,311 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA274.76, 519.234 
Publication Timeline
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Most widely held works about
Krishna B Athreya
Most widely held works by
Krishna B Athreya
Measure theory and probability theory by
Krishna B Athreya(
)
22 editions published between 2006 and 2010 in English and held by 675 WorldCat member libraries worldwide
"This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph. D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph. D. students as it provides full coverage of topics such as the construction of LebesgueStieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, RadonNikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and FubiniTonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph. D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 613) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the LevyCramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 1418) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes."Publisher's website
22 editions published between 2006 and 2010 in English and held by 675 WorldCat member libraries worldwide
"This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph. D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph. D. students as it provides full coverage of topics such as the construction of LebesgueStieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, RadonNikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and FubiniTonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph. D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 613) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the LevyCramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 1418) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes."Publisher's website
Branching processes by
Krishna B Athreya(
Book
)
35 editions published between 1972 and 2012 in 4 languages and held by 617 WorldCat member libraries worldwide
The GaltonWatson process. Potential theory. One dimensional continuous time Markov branching processes. Agedependent processes. Multitype branching processes. Special processes
35 editions published between 1972 and 2012 in 4 languages and held by 617 WorldCat member libraries worldwide
The GaltonWatson process. Potential theory. One dimensional continuous time Markov branching processes. Agedependent processes. Multitype branching processes. Special processes
Probability, statistics, and mathematics : papers in honor of Samuel Karlin by
Samuel Karlin(
Book
)
8 editions published between 1989 and 2014 in English and held by 321 WorldCat member libraries worldwide
Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin is a collection of papers dealing with probability, statistics, and mathematics. Conceived in honor of Polishborn mathematician Samuel Karlin, the book covers a wide array of topics, from the secondorder moments of a stationary Markov chain to the exponentiality of the local time at hitting times for reflecting diffusions. Smoothed limit theorems for equilibrium processes are also discussed.<br><br>Comprised of 24 chapters, this book begins with an introduction to the secondorder moments of a stationary Markov chain
8 editions published between 1989 and 2014 in English and held by 321 WorldCat member libraries worldwide
Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin is a collection of papers dealing with probability, statistics, and mathematics. Conceived in honor of Polishborn mathematician Samuel Karlin, the book covers a wide array of topics, from the secondorder moments of a stationary Markov chain to the exponentiality of the local time at hitting times for reflecting diffusions. Smoothed limit theorems for equilibrium processes are also discussed.<br><br>Comprised of 24 chapters, this book begins with an introduction to the secondorder moments of a stationary Markov chain
Classical and modern branching processes by
Krishna B Athreya(
Book
)
12 editions published in 1997 in English and held by 274 WorldCat member libraries worldwide
This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 199394 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes
12 editions published in 1997 in English and held by 274 WorldCat member libraries worldwide
This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 199394 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes
Advances in crystallization from solutions(
Book
)
2 editions published in 1984 in English and held by 229 WorldCat member libraries worldwide
2 editions published in 1984 in English and held by 229 WorldCat member libraries worldwide
Probability, statistics, and their applications : papers in honor of Rabi Bhattacharya by
R. N Bhattacharya(
Book
)
13 editions published between 2003 and 2008 in English and held by 92 WorldCat member libraries worldwide
This ebook is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press
13 editions published between 2003 and 2008 in English and held by 92 WorldCat member libraries worldwide
This ebook is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press
Convergence of the age distribution in the onedimensional supercritical agedependent branching process by
Krishna B Athreya(
Book
)
2 editions published in 1975 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1975 in English and held by 8 WorldCat member libraries worldwide
Stochastic processes and related topics by
Madan Lal Puri(
Book
)
1 edition published in 1975 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 8 WorldCat member libraries worldwide
Measure theory by
Krishna B Athreya(
Book
)
1 edition published in 2006 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 7 WorldCat member libraries worldwide
Limit theorems for a branching process with disasters by
Krishna B Athreya(
Book
)
1 edition published in 1975 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 6 WorldCat member libraries worldwide
Probability theory by
Krishna B Athreya(
Book
)
2 editions published in 2006 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 6 WorldCat member libraries worldwide
Estimation theory for continuoustime branching processes by
Krishna B Athreya(
Book
)
1 edition published in 1975 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 6 WorldCat member libraries worldwide
Stochastic iteration by
Krishna B Athreya(
Book
)
6 editions published in 1974 in English and Undetermined and held by 5 WorldCat member libraries worldwide
6 editions published in 1974 in English and Undetermined and held by 5 WorldCat member libraries worldwide
Random logistic maps II : the critical case by
Krishna B Athreya(
Book
)
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
A simple proof of a result of Kesten and Stigum on supercritical multitype GaltonWatson branching processes by
Krishna B Athreya(
Book
)
4 editions published in 1969 in English and held by 4 WorldCat member libraries worldwide
The paper gives a new and simple proof of a key result due to Kesten and Stigum in the theory of supercritical multitype GaltonWatson branching process
4 editions published in 1969 in English and held by 4 WorldCat member libraries worldwide
The paper gives a new and simple proof of a key result due to Kesten and Stigum in the theory of supercritical multitype GaltonWatson branching process
On the supercritical BellmanHarris process with finite mean by
Krishna B Athreya(
Book
)
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
On the equivalence of conditions on a branching process in continuous time and on its offspring distribution by
Krishna B Athreya(
Book
)
4 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide
The paper shows under very general conditions on a convex functions phi E phi(x(t)) <infinity if and only if Summation over j of (phi(j)p sub j) <infinity where X(t) is a continuous time branching (Markov or age dependent) process with offspring generating function h(z) = Summation from j=0 to j = infinity of ((p sub j) (z superscript j)). (Author)
4 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide
The paper shows under very general conditions on a convex functions phi E phi(x(t)) <infinity if and only if Summation over j of (phi(j)p sub j) <infinity where X(t) is a continuous time branching (Markov or age dependent) process with offspring generating function h(z) = Summation from j=0 to j = infinity of ((p sub j) (z superscript j)). (Author)
On the supercritical one dimensional age dependent branching processes by
Krishna B Athreya(
Book
)
4 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide
For an age dependent branching process (Z(t);t> or = 0) with mean function m(t) we show Z(t)/(m(t)) converges in distribution to a nondegenerate limit law if and only if the sum of (j log j(p sub j) <infinity) where (p sub j) is the offspring distribution
4 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide
For an age dependent branching process (Z(t);t> or = 0) with mean function m(t) we show Z(t)/(m(t)) converges in distribution to a nondegenerate limit law if and only if the sum of (j log j(p sub j) <infinity) where (p sub j) is the offspring distribution
A note on a functional equation arising in GaltonWatson branching processes by
Krishna B Athreya(
Book
)
3 editions published in 1969 in English and held by 3 WorldCat member libraries worldwide
The functional equation phi(mu) = h(phi(u)) where h(s) = the summation from j=o to infinity of p subj S supj is a p.g.f. with 1<m=h primed (1 ) <infinity and phi(u) = the integral from o to infinity of e to the ( ut) power dF(t) where F(t) is a nondecreasing right continuous function with F(0 ) = 0 and F(+ infinity) = 1 arises in GaltonWatson process in a natural way. One proves here that for any p>or= 0, the integral from o to infinity of t/logt/supp dF(t)<infinity if and only if the summation from j=2 to infinity of j((log j) sup(p+1))(p subj)<infinity. This unifies several results in the literature on supercritical GaltonWatson process. One generalizes this to an age dependent branching process case as well. (Author)
3 editions published in 1969 in English and held by 3 WorldCat member libraries worldwide
The functional equation phi(mu) = h(phi(u)) where h(s) = the summation from j=o to infinity of p subj S supj is a p.g.f. with 1<m=h primed (1 ) <infinity and phi(u) = the integral from o to infinity of e to the ( ut) power dF(t) where F(t) is a nondecreasing right continuous function with F(0 ) = 0 and F(+ infinity) = 1 arises in GaltonWatson process in a natural way. One proves here that for any p>or= 0, the integral from o to infinity of t/logt/supp dF(t)<infinity if and only if the summation from j=2 to infinity of j((log j) sup(p+1))(p subj)<infinity. This unifies several results in the literature on supercritical GaltonWatson process. One generalizes this to an age dependent branching process case as well. (Author)
Limit theorems for multitype continuous time Markov branching processes and some classical urn schemes by
Krishna B Athreya(
)
2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide
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Related Identities
 Lahiri, S. N. (Soumendra Nath)
 Ney, Peter 1930
 Iglehart, Donald L. 1933 Editor
 Anderson, T. W. (Theodore Wilbur) 19182016 Author Editor
 Karlin, Samuel 19232007 Honoree
 Jagers, Peter 1941 Editor
 Youngquist, Gordon R.
 Bhattacharya, R. N. (Rabindra Nath) 1937 Bibliographic antecedent Honoree Author Dedicatee
 Kaplan, Norman L.
 Summer Research Institute
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Associated Subjects
Age distribution (Demography) Branching processes Canada College teachers Computer science Convergence Crystallization Distribution (Probability theory) Econometrics Editors Estimation theory Fluid dynamics Functional equations Integrals, Generalized Integration, Functional Iterative methods (Mathematics) Karlin, Samuel, Limit theorems (Probability theory) Markov processes Mathematical statistics Mathematics Measure theory Operations research Probabilities Research Scientists Stochastic processes United States
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Alternative Names
Athreya, K.
Athreya, K. 1939
Athreya, K.B.
Athreya, K. B. 1939
Athreya, K. B. (Krishna B.), 1939
Athreya, K. (Krishna), 1939
Athreya, Krishna.
Athreya, Krishna 1939
Athreya, Krishna B.
Athreya, Krishna Balasundaram.
Athreya, Krishna Balasundaram, 1939
Krishna B. Athreya Indian mathematical statistician
Krishna Balasundaram Athreya.
Krishna Balasundaram Athreya 1939....
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