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高斯过程的轨道性质(影印版)

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高斯过程的轨道性质(影印版)

最 低 价:¥22.50

定 价:¥25.00

作 者:Lin Zheng-yan,Lu Chuan-rong,Zhang Li-xin

出 版 社:浙江大学出版社

出版时间:2001 年9月

I S B N:7308027244

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内容简介

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, these fundamental contributions have been the principal guidelines in the literature on path properties of general Gaussian and many other related stochastic
  

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目录

introduction
chapter 1 some basic results on gaussian variables and
gaussian processes
1.1 tail behavior of the supremum of a gaussian
process
1.2 comparison theorems
chapter 2 moduli of continuity and limit behavior of large
increments for gaussian processes
2.1 the continuity of gaussian processes
2.2 fractional wiener processes
2.3 large increments of a two-parameter wiener
process
2.4 two-parameter fractional levy-wiener processes
2.5 two-parameter ornstein-uhlenbeck process
2.6 kernel generated two-parameter gaussian processes
2.7 moduli of continuity for local times of gaussian
processes
chapter 3 moduli of continuity and large increments
for infinite dimensional gaussian processes
3.1 continuity of/p-valued gaussian processes
.3.2 the increments for b-valued stochastic processes
3.3 the increments for/p-valued gaussian processes
3.4 the increments for loo-valued gaussian processes
chapter 4 the law of the iterated logarithm and almost
sure limit inferior of increments for gaussian
processes
4.1 the strassen laws of the iterated logarithm and
its rates for gaussian processes
4.2 erd6s-revesz's law of the iterated logarithm for
gaussian processes
4.3 the small ball probability and chung's law of the
iterated logarithm of gaussian processes
4.4 the small ball probability and chung's law of the
iterated logarithm of gaussian fields
4.5 liminfs for increments of gaussian processes
4.6 liminfs for two-parameter gaussian processes
chapter 5 other path properties of gaussian processes
5.1 the p-variation of gaussian processes
5.2 the fractal nature of image and graph of gaussian
fields
5.3 the fractal nature of increments of lp-valued
gaussian processes
5.4 the fractal nature of increments of the infinite
series of ornstein-uhlenbeck processes related
to the chung type lil
references
subject index

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