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Asymptotic Methods in Stochastics: Festschrift for Miklós Csörgő
Edited by: Lajos Horváth, University of Utah, Salt Lake City, UT, and Barbara Szyszkowicz, Carleton University, Ottawa, ON, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2004; 530 pp; hardcover
Volume: 44
ISBN-10: 0-8218-3561-0
ISBN-13: 978-0-8218-3561-6
List Price: US$142
Member Price: US$113.60
Order Code: FIC/44
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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 self-normalized 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 co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate 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
  • E. Csáki, A. Földes, and Z. Shi -- Our joint work with Miklós Csörgő
  • D. Khoshnevisan -- Brownian sheet and quasi-sure analysis
  • G. Peccati and M. Yor -- Hardy's inequality in \(L^2([0,1])\) and principal values of Brownian local times
  • G. Peccati and M. 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. J. Bhansali, M. P. Holland, and P. S. Kokoszka -- Chaotic maps with slowly decaying correlations and intermittency
  • Y. Davydov and V. Paulauskas -- Recent results on \(p\)-stable convex compact sets with applications
  • Y. Davydov and R. Zitikis -- Convex rearrangements of random elements
  • D. A. Dawson, L. G. Gorostiza, and A. Wakolbinger -- Hierarchical random walks
  • K. A. Ross and Q.-M. Shao -- On Helgason's number and Khintchine's inequality
Complete convergence of renewal counting processes and bootstrap means
  • A. Gut and J. Steinebach -- Convergence rates and precise asymptotics for renewal counting processes and some first passage times
  • S. Csörgő -- On the complete convergence of bootstrap means
Weak convergence of random size sums, almost sure stability of weighted maxima
  • I. Ćwiklińska and Z. Rychlik -- Weak convergence of random sums and maximum random sums under nonrandom norming
  • R. J. Tomkins -- Criteria for the almost sure stability of weighted maxima of bounded i.i.d. random variables
Procedures for detecting changes in statistical models
  • M. Hušková -- Permutation principle and bootstrap in change point analysis
  • E.-E. A. A. Aly -- Change point detection based on \(L\)-statistics
  • E. Atenafu and E. Gombay -- Sequential tests for change in the parameters of nested random effects model
  • M. Orasch -- Using U-statistics based processes to detect multiple change-points
Statistical inference via conditional quantiles, cumulative sums, multinomial samples, and empirical processes
  • E. Parzen -- Statistical methods learning and conditional quantiles
  • M. D. Burke -- Testing regression models: A strong martingale approach
  • A. R. Dabrowski and H. Dehling -- Conditional distribution of the H-coefficient in nonparametric unfolding models
  • K. Ghoudi and B. Rémillard -- Empirical processes based on pseudo-observations II: The multivariate case
Applications to economics
  • I. Berkes, L. Horváth, and P. Kokoszka -- Probabilistic and statistical properties of GARCH processes
  • R. Kulperger -- Stochastic finance: Discrete time processes and risk neutral pricing
  • D. L. McLeish -- Estimating the correlation of processes using extreme values
  • H. Yu -- Analyzing residual processes of (G)ARCH time series models
Self-normalized partial sums processes
  • M. Csörgő, B. Szyszkowicz, and Q. Wang -- On weighted approximations and strong limit theorems for self-normalized partial sums processes
  • Q. Wang -- On Darling-Erdős type theorems for self-normalized sums
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