高斯过程的轨道性质及其相关问题

摘要

 Chapterl Increments of some Gaussl an processes. Introduction The dlmendonJ Gausslan processes The valued muhLparameter Gausslan processes;Chapter 11 Functional limit theorems for one．dimensional FBM and OU processes;Chapter Ill Funotional limit theorem for dimensional FBM;Chapter IV Funotional limit theorem for selfsimilar Gaussian processes In Holder type norm;Chapter V Convergence of random variables.

目录

前言

Chapter Ⅰ Increments of some Gaussian processes

1.1. Introduction

1.2. The d-dimensional Gaussian processes

1.3. The lp-valued multi-parameter Gaussian processes

Chapter Ⅱ Functional limit theorems for one-dimensional FBM and OU processes

2.1. The increments of one-dimensional FBM in sup-norm

2.2. OU processes in H(o)lder norm

Chapter Ⅲ Functional limit theorems for d-dimensional FBM

3.1. Introduction

3.2. Modulus of continuity

3.3. Functional large increments

Chapter Ⅳ Functional limit theorem for self-similar Gaussian processes in H(o)lder type norm

4.1. Introduction

4.2. Modulus of continuity for self-similar Gaussian processes

4.3. LIL for self-similar Gaussian processes

Chapter Ⅴ Convergence of random variables

5.1. Precise rates in the law of logarithm for the moment convergence of iid random variablesvs

5.2. Asymptotics for self-normalized random products of sums of iid random variables

References

List of papers

Acknowledgements