**Fields Institute Communications**

Volume: 44;
2004;
530 pp;
Hardcover

MSC: Primary 60; 62;

Print ISBN: 978-0-8218-3561-6

Product Code: FIC/44

List Price: $150.00

Individual Member Price: $120.00

**Electronic ISBN: 978-1-4704-3078-8
Product Code: FIC/44.E**

List Price: $150.00

Individual Member Price: $120.00

# Asymptotic Methods in Stochastics: Festschrift for Miklós Csörgő

Share this page *Edited by *
*Lajos Horváth; Barbara Szyszkowicz*

A co-publication of the AMS and Fields Institute

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).

#### Table of Contents

# Table of Contents

## Asymptotic Methods in Stochastics: Festschrift for Miklos Csorgo

- Cover Cover11
- Title page iii4
- Contents v6
- Miklós Csörgő ix10
- Preface xi12
- Path properties of stochastic processes 116
- Our joint work with Miklós Csörgő 318
- Brownian sheet and quasi-sure analysis 2540
- Hardy’s inequality in 𝐿²([0,1]) and principal values of Brownian local times 4964
- Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge 7590
- Tell me the values of a Wiener at integers, I tell you its local time 89104
- Probability theory with applications 97112
- Chaotic maps with slowly decaying correlations and intermittency 99114
- Recent results on 𝑝-stable convex compact sets with applications 127142
- Convex rearrangements of random elements 141156
- Hierarchical random walks 173188
- On Helgason’s number and Khintchine’s inequality 195210
- Complete convergence of renewal counting processes and bootstrap means 203218
- Convergence rates and precise asymptotics for renewal counting processes and some first passage times 205220
- On the complete convergence of bootstrap means 229244
- Weak convergence of random size sums, almost sure stability of weighted maxima 243258
- Weak convergence of random sums and maximum random sums under nonrandom norming 245260
- Criteria for the almost sure stability of weighted maxima of bounded i.i.d. random variables 265280
- Procedures for detecting changes in statistical models 271286
- Permutation principle and bootstrap in change point analysis 273288
- Change point detection based on 𝐿-statistics 293308
- Sequential tests for change in the parameters of nested random effects model 301316
- Using U-statistics based processes to detect multiple change-points 315330
- Statistical inference via conditional quantiles, cumulative sums, multinomial samples, and empirical processes 335350
- Statistical methods learning and conditional quantiles 337352
- Testing regression models: A strong martingale approach 351366
- Conditional distribution of the H-coefficient in nonparametric unfolding models 367382
- Empirical processes based on pseudo-observations II: The multivariate case 381396
- Applications to economics 407422
- Probabilistic and statistical properties of GARCH processes 409424
- Stochastic finance: Discrete time processes and risk neutral pricing 431446
- Estimating the correlation of processes using extreme values 447462
- Analyzing residual processes of (G)ARCH time series models 469484
- Self-normalized partial sums processes 487502
- On weighted approximations and strong limit theorems for self-normalized partial sums processes 489504
- On Darling-Erdős type theorems for self-normalized sums 523538
- Back Cover Back Cover1546

#### Readership

Graduate students and research mathematicians interested in probability theory, stochastic processes, mathematical statistics, and applications of these mathematical and statistical sciences.