Description
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.
Chapter
Path properties of stochastic processes
Our joint work with Miklós Csörgő
Brownian sheet and quasi-sure analysis
Hardy’s inequality in 𝐿²([0,1]) and principal values of Brownian local times
Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge
Tell me the values of a Wiener at integers, I tell you its local time
Probability theory with applications
Chaotic maps with slowly decaying correlations and intermittency
Recent results on 𝑝-stable convex compact sets with applications
Convex rearrangements of random elements
Hierarchical random walks
On Helgason’s number and Khintchine’s inequality
Complete convergence of renewal counting processes and bootstrap means
Convergence rates and precise asymptotics for renewal counting processes and some first passage times
On the complete convergence of bootstrap means
Weak convergence of random size sums, almost sure stability of weighted maxima
Weak convergence of random sums and maximum random sums under nonrandom norming
Criteria for the almost sure stability of weighted maxima of bounded i.i.d. random variables
Procedures for detecting changes in statistical models
Permutation principle and bootstrap in change point analysis
Change point detection based on 𝐿-statistics
Sequential tests for change in the parameters of nested random effects model
Using U-statistics based processes to detect multiple change-points
Statistical inference via conditional quantiles, cumulative sums, multinomial samples, and empirical processes
Statistical methods learning and conditional quantiles
Testing regression models: A strong martingale approach
Conditional distribution of the H-coefficient in nonparametric unfolding models
Empirical processes based on pseudo-observations II: The multivariate case
Applications to economics
Probabilistic and statistical properties of GARCH processes
Stochastic finance: Discrete time processes and risk neutral pricing
Estimating the correlation of processes using extreme values
Analyzing residual processes of (G)ARCH time series models
Self-normalized partial sums processes
On weighted approximations and strong limit theorems for self-normalized partial sums processes
On Darling-Erdős type theorems for self-normalized sums