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Title page

Contents

Miklós Csörgő

Preface

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

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