高斯过程的轨道性质（影印版）

　　It pleases me very much to have opportunity for introducing this remarkable book on fine analytic path properties of Gaussian and related processes. In a series of papers in the nineteen twenties， Norbert Wiener undertook a mathematical analysis of Brownian motion.He showed that， except for a set of cases of probability zero' （with respect to what has been called Wiener measure since）， all the Brownian motion paths were continuous non-differentiable curves.In the forties，Paul Levy proved his famous modulus of continuity theorem that established "the exact rate of continuity" for almost all sample paths of Brownian motion （Wiener process ）.Ever since，thesefundamental contributions have been the principal guidelines in the literature on path properties of general Gaussian and many other related stochastic

暂缺《高斯过程的轨道性质（影印版）》作者简介

Introduction
Chapter1SomeBasicResultsonGaussianVariablesand
GaussianProcesses
1.1TailBehavioroftheSupremumofaGaussian
Process
1.2ComparisonTheorems
Chapter2ModuliofContinuityandLimitBehaviorofLarge
IncrementsforGaussianProcesses
2.1TheContinuityofGaussianProcesses
2.2FractionalWienerProcesses
2.3LargeIncrementsofaTwo-parameterWiener
Process
2.4Two-parameterFractionalLevy-WienerProcesses
2.5Two-parameterOrnstein-UhlenbeckProcess
2.6KernelGeneratedTwo-parameterGaussianProcesses
2.7ModuliofContinuityforLocalTimesofGaussian
Processes
Chapter3ModuliofContinuityandLargeIncrements
forInfiniteDimensionalGaussianProcesses
3.1Continuityof/P-valuedGaussianProcesses
3.2TheIncrementsforB-valuedStochasticProcesses
3.3TheIncrementsfor/P-valuedGaussianProcesses
3.4TheIncrementsforloo-valuedGaussianProcesses
Chapter4TheLawoftheIteratedLogarithmandAlmost
SureLimitInferiorofIncrementsforGaussian
Processes
4.1TheStrassenLawsoftheIteratedLogarithmand
ItsRatesforGaussianProcesses
4.2Erd6s-Revesz'sLawoftheIteratedLogarithmfor
GaussianProcesses
4.3TheSmallBallProbabilityandChung'sLawofthe
IteratedLogarithmofGaussianProcesses
4.4TheSmallBallProbabilityandChung'sLawofthe
IteratedLogarithmofGaussianFields
4.5LiminfsforIncrementsofGaussianProcesses
4.6LiminfsforTwo-parameterGaussianProcesses
Chapter5OtherPathPropertiesofGaussianProcesses
5.1Thep-variationofGaussianProcesses
5.2TheFractalNatureofImageandGraphofGaussian
Fields
5.3TheFractalNatureofIncrementsoflP-valued
GaussianProcesses
5.4TheFractalNatureofIncrementsoftheInfinite
SeriesofOrnstein-UhlenbeckProcessesRelated
totheChungTypeLIL
REFERENCES
SubjectIndex