随机过程用的极限定理-第2版

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作者：（法）杰克德　著

出版社：世界图书出版公司

本类榜单：自然科学

分类：自然科学 > 数学 > 概率论与数理统计

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ISBN：9787510061387
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：24开
页数：660
出版时间：2013-10-01
条形码：9787510061387 ; 978-7-5100-6138-7

本书特色

杰克德编著的《随机过程用的极限定理（第2版）》的**版成为学习随机过程函数收敛的**读物，这部科学巨着终于出第2版了，仍然延续了第1版的风格，但增加了不少新的知识，在厚度上的增加了将近50面。第1版面世后，可预测的一致胎紧性有了很大的进展，所以书中也做了全面的更新。本书仍然是学习随机过程的一本不可或缺的参考书。目次：随机过程一般概念；半鞅和独立增量过程的特征；鞅问题和测量改变；Hellinger过程、绝对连续和测度奇异性；绝对连续和奇异的可预测准则；近邻性、完全独立和变分收敛；Skorokhod拓扑和过程收敛；具有独立增量的过。

内容简介

《随机过程用的极限定理(第2版)(英文)》讲述Apart from correcting a number of printing mistakes,and some mathematical inaccuracies as well,this second edition contains some new material: indeed,during the fifteen years elapsed since the first edition came out,a large number of new results concerning limit theorems have of course been proved by many authors,and more generally mathematical life has been going on.This gave us the feeling that some of the material in the first edition was perhaps not as important as we thought at the time,while there were some neglected topics which have in fact proved to be very useful in various applications.So perhaps a totally new book would have been a good thing to write.Our natural laziness prevented us to do that,but we have felt compelled to fill in the most evident holes in this book.This has been done in the most painless way for us,and also for the reader acquainted with the first edition （at least we hope so ...）.That is all new material has been added at the end of preexisting chapters.

chapter i. the general theory of stochastic processes,
semimartingales and stochastic integrals
1. stochastic basis, stopping times, optionala-field,martingales
　1a. stochastic basis
　lb. stopping times
　lc. the optional a-field
　ld. the localization procedure
　1e. martingales
　1f. the discrete case
2. predictable a-field, predictable times
　2a. the predictable a-field
　2b. predictable times
　2c. totally inaccessible stopping times
　2d. predictable projection
　2e. the discrete case
3. increasing processes　
　3a. basic properties
　3b. do, b-meyer decomposition and compensatorsof increasingprocesses
　3c. lenglart domination property
　3d. the discrete case
4. semimartingales and stochastic integrals
　4a. locally square-integrable martingales
　4b. decompositions of a local martingale
　4c. semimartingales
　4d. construction of the stochastic integral
　4e. quadratic variation ofa semimartingale and ito's formula
　4f. dol6ans-dade exponential formula
　4g. the discrete case
chapter ii. characteristics of semimartingales and processes　withindependent increments
1. random measures
　1a. general random measures
　lb. integer-valued random measures
　1c. a fundamental example: poisson measures
　1d. stochastic integral with respect to a random measure
2. characteristics of semimartingales
　2a. definition of the characteristics
　2b. integrability and characteristics
　2c. a canonical representation for semimartingales
　2d. characteristics and exponential formula
3. some examples
　3a. the discrete case
　3b. more on the discrete case
　3c. the "one-point" point process and empirical processes
4. semimartingales with independent increments
　4a. wiener processes
　4b. poisson processes and poisson random measures
　4c. processes with independent increments andsemimartingales
　4d. gaussian martingales
5. processes with independent increments
　which are not semimartingales
　5a. the results
　5b. the proofs
6. processes with conditionally independent increments
7. progressive conditional continuous piis
8. semimartingales, stochastic exponential and stochasticlogarithm.
　8a. more about stochastic exponential and stochasticlogarithm.
　8b. multiplicative decompositions andexponentially　special　semimartingales
chapter iii. martingale problems and changes of measures
1. martingale problems and point processes
　1a. general martingale problems
　1b. martingale problems and random measures
　1c. point processes and multivariate point processes
……

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