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Hardcover ISBN:  9780821835616 
Product Code:  FIC/44 
List Price:  $167.00 
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AMS Member Price:  $133.60 
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Product Code:  FIC/44.E 
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Hardcover ISBN:  9780821835616 
eBook ISBN:  9781470430788 
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Book DetailsFields Institute CommunicationsVolume: 44; 2004; 530 ppMSC: Primary 60; 62
This volume, honoring over forty years of Miklós Csörgő's work in probability and statistics, reflects the state of current research. It offers a comprehensive collection of surveys introducing new results with complete proofs and expository papers giving an historic overview.
Contributions were made by an international group of experts. The book covers the following topics: path properties of stochastic processes, probability theory with applications, complete convergence of renewal counting processes and bootstrap means, weak convergence of random size sums, almost sure stability of weighted maxima, procedures for detecting changes in statistical models, statistical inference via conditional quantiles, cumulative sums, multinomial samples, empirical processes, applications to economics, and selfnormalized partial sums processes. The section, "Applications to Economics", deals primarily with applications of stochastics to financial time series models.
The book is suitable for graduate students and researchers interested in probability theory, stochastic processes, mathematical statistics, and applications of these mathematical/statistical sciences.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians interested in probability theory, stochastic processes, mathematical statistics, and applications of these mathematical and statistical sciences.

Table of Contents

Path properties of stochastic processes

Endre Csáki, Antónia Földes and Zhan Shi — Our joint work with Miklós Csörgő

Davar Khoshnevisan — Brownian sheet and quasisure analysis

Giovanni Peccati and Marc Yor — Hardy’s inequality in $L^2([0,1])$ and principal values of Brownian local times

Giovanni Peccati and Marc Yor — Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge

P. Révész — Tell me the values of a Wiener at integers, I tell you its local time

Probability theory with applications

R. Bhansali, M. Holland and P. Kokoszka — Chaotic maps with slowly decaying correlations and intermittency

Youri Davydov and Vygantas Paulauskas — Recent results on $p$stable convex compact sets with applications

Youri Davydov and Ričardas Zitikis — Convex rearrangements of random elements

D. Dawson, L. Gorostiza and A. Wakolbinger — Hierarchical random walks

Kenneth Ross and QiMan Shao — On Helgason’s number and Khintchine’s inequality

Complete convergence of renewal counting processes and bootstrap means

Allan Gut and Josef Steinebach — Convergence rates and precise asymptotics for renewal counting processes and some first passage times

Sándor Csörgő — On the complete convergence of bootstrap means

Weak convergence of random size sums, almost sure stability of weighted maxima

Iwona Ćwiklińska and Zdzisław Rychlik — Weak convergence of random sums and maximum random sums under nonrandom norming

R. Tomkins — Criteria for the almost sure stability of weighted maxima of bounded i.i.d. random variables

Procedures for detecting changes in statistical models

Marie Hušková — Permutation principle and bootstrap in change point analysis

EmadEldin Aly — Change point detection based on $L$statistics

Eshetu Atenafu and Edit Gombay — Sequential tests for change in the parameters of nested random effects model

Markus Orasch — Using Ustatistics based processes to detect multiple changepoints

Statistical inference via conditional quantiles, cumulative sums, multinomial samples, and empirical processes

Emanuel Parzen — Statistical methods learning and conditional quantiles

Murray Burke — Testing regression models: A strong martingale approach

André Dabrowski and Herold Dehling — Conditional distribution of the Hcoefficient in nonparametric unfolding models

Kilani Ghoudi and Bruno Rémillard — Empirical processes based on pseudoobservations II: The multivariate case

Applications to economics

Itsván Berkes, Lajos Horváth and Piotr Kokoszka — Probabilistic and statistical properties of GARCH processes

Reg Kulperger — Stochastic finance: Discrete time processes and risk neutral pricing

Don McLeish — Estimating the correlation of processes using extreme values

Hao Yu — Analyzing residual processes of (G)ARCH time series models

Selfnormalized partial sums processes

Miklós Csörgő, Barbara Szyszkowicz and Qiying Wang — On weighted approximations and strong limit theorems for selfnormalized partial sums processes

Qiying Wang — On DarlingErdős type theorems for selfnormalized sums


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This volume, honoring over forty years of Miklós Csörgő's work in probability and statistics, reflects the state of current research. It offers a comprehensive collection of surveys introducing new results with complete proofs and expository papers giving an historic overview.
Contributions were made by an international group of experts. The book covers the following topics: path properties of stochastic processes, probability theory with applications, complete convergence of renewal counting processes and bootstrap means, weak convergence of random size sums, almost sure stability of weighted maxima, procedures for detecting changes in statistical models, statistical inference via conditional quantiles, cumulative sums, multinomial samples, empirical processes, applications to economics, and selfnormalized partial sums processes. The section, "Applications to Economics", deals primarily with applications of stochastics to financial time series models.
The book is suitable for graduate students and researchers interested in probability theory, stochastic processes, mathematical statistics, and applications of these mathematical/statistical sciences.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in probability theory, stochastic processes, mathematical statistics, and applications of these mathematical and statistical sciences.

Path properties of stochastic processes

Endre Csáki, Antónia Földes and Zhan Shi — Our joint work with Miklós Csörgő

Davar Khoshnevisan — Brownian sheet and quasisure analysis

Giovanni Peccati and Marc Yor — Hardy’s inequality in $L^2([0,1])$ and principal values of Brownian local times

Giovanni Peccati and Marc Yor — Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge

P. Révész — Tell me the values of a Wiener at integers, I tell you its local time

Probability theory with applications

R. Bhansali, M. Holland and P. Kokoszka — Chaotic maps with slowly decaying correlations and intermittency

Youri Davydov and Vygantas Paulauskas — Recent results on $p$stable convex compact sets with applications

Youri Davydov and Ričardas Zitikis — Convex rearrangements of random elements

D. Dawson, L. Gorostiza and A. Wakolbinger — Hierarchical random walks

Kenneth Ross and QiMan Shao — On Helgason’s number and Khintchine’s inequality

Complete convergence of renewal counting processes and bootstrap means

Allan Gut and Josef Steinebach — Convergence rates and precise asymptotics for renewal counting processes and some first passage times

Sándor Csörgő — On the complete convergence of bootstrap means

Weak convergence of random size sums, almost sure stability of weighted maxima

Iwona Ćwiklińska and Zdzisław Rychlik — Weak convergence of random sums and maximum random sums under nonrandom norming

R. Tomkins — Criteria for the almost sure stability of weighted maxima of bounded i.i.d. random variables

Procedures for detecting changes in statistical models

Marie Hušková — Permutation principle and bootstrap in change point analysis

EmadEldin Aly — Change point detection based on $L$statistics

Eshetu Atenafu and Edit Gombay — Sequential tests for change in the parameters of nested random effects model

Markus Orasch — Using Ustatistics based processes to detect multiple changepoints

Statistical inference via conditional quantiles, cumulative sums, multinomial samples, and empirical processes

Emanuel Parzen — Statistical methods learning and conditional quantiles

Murray Burke — Testing regression models: A strong martingale approach

André Dabrowski and Herold Dehling — Conditional distribution of the Hcoefficient in nonparametric unfolding models

Kilani Ghoudi and Bruno Rémillard — Empirical processes based on pseudoobservations II: The multivariate case

Applications to economics

Itsván Berkes, Lajos Horváth and Piotr Kokoszka — Probabilistic and statistical properties of GARCH processes

Reg Kulperger — Stochastic finance: Discrete time processes and risk neutral pricing

Don McLeish — Estimating the correlation of processes using extreme values

Hao Yu — Analyzing residual processes of (G)ARCH time series models

Selfnormalized partial sums processes

Miklós Csörgő, Barbara Szyszkowicz and Qiying Wang — On weighted approximations and strong limit theorems for selfnormalized partial sums processes

Qiying Wang — On DarlingErdős type theorems for selfnormalized sums