Convergence of stochastic processes

Cover
Title page
Preface
Notation
I: Functionals on stochastic processes
II: Uniform convergence of empirical measures
Uniformity and consistency
Direct approximation
The combinatorial method
Classes of sets with polynomial discrimination
Classes of functions
Rates of convergence
Notes
Problems
III: Convergence in distribution in Euclidean spaces
IV: Convergence in distribution in metric spaces
Measurability
The continuous mapping theorem
Representation by almost surely convergent sequences
Coupling
Weakly convergent subsequences
Notes
Problems
V: The uniform metric on spaces of cadlag functions
Approximation of stochastic processes
Empirical processes
Existence of brownian bridge and brownian motion
Processes with independent increments
Infinite time scales
Functionals of brownian motion and brownian bridge
Notes
Problems
VI: The Skorokhod metric on D[0,∞)
VII: Central limit theorems
Stochastic equicontinuity
Chaining
Gaussian processes
Random covering numbers
Empirical central limit theorems
Restricted chaining
Notes
Problems
VIII: Martingales
A: Stochastic-order symbols
B: Exponential inequalities
C: Measurability
References
Author index
Subject index