扩散过程及其样本轨道
2010-1
世界图书出版公司
伊藤清
321
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对与扩散现象有关的随机过程产生持久而深刻的影响。不少数学家受益于《扩散过程及其样本轨道(英文版)》一维和多维扩散过程的描述和独到的布朗运动数学见解。传承这一系列书的风格，行文简洁流畅。每章节后面都配有问题并有部分解答，很适合作为教材和自学用书。目次：标准布朗运动；布朗局部时间；一般一维扩散；生成元；局部时间和逆时间序列；多维布朗运动；多维扩散简述。
PrerequisitesChapter 1. The standard BRowNian motion1.1. The standard random walk1.2. Passage times for the standard random walk1.3. HINCIN‘S proof of the DE MOIVRE-LAPLACE limit theorem1.4. The standard BROWNian motion1.5. P. LEVY’s cotruction1.6. Strict MAgKOV character1.7. Passage times for the standard BgowNian motionNote 1： Homogeneous differential processes with increasing paths1.8. KOLMOGOROV‘S test and the law of the iterated logarithm1.9. P. LEVY’S HOLDER condition1.10. Approximating the BgowNian motion by a random walkChapter 2. BROWNian local times2.1. The reflecting BRowNian motion2.2. P. LEVY‘S local time2.3. Elastic BgowNian motion2.4. t+ and down-crossings2.5. t+ as HAUSDORFF-BESICOVITCH 1/2-dimeional measureNote 1： SubmartingalesNote 2： HAUSDORFF measure and dimeion2.6. Kxc’s formula for BRowNian funetionals2.7. BESSEL processes2.8. Standard BRowNian local time2.9. BRowNian excuio2.10. Application of the BESSEL process to BROWNian excuio2.11. A time substitutionChapter 3. The general t-dimeional diffusion3.t. Definition3.2. MARKOV times3.3. Matching numbe3.4. Singular points3.5. Decomposing the general diffusion into simple pieces3.6. GREEN operato and the spaceD3.7. Generato3.8. Generato continued3.9. Stopped diffusionChapter 4. Generato4.1. A general view4.2. as local differential operator： coervative non-singular case4.3. as local differential operator： general non-singular case4.4. A second proof4.5. at an isolated singular point4.6. Solving4.7. as global differential operator： non-singular case4.8. on the shunts4.9. as global differential operator： singular case4.10. Passage timesNote 1： Differential processes with increasing paths4.ft. Eigen-differential expaio for GREEN functio and traitiondeities4.12. KOLMOGOROV‘S testChapter 5. Time changes and killing5.1. Cotruction of sample paths： a general view5.2. Time changes5.3. Time changes5.4. Local times5.5. Subordination and chain rule5.6. Killing times5.7. FELLER’S BROWNlan motio5.8. IKEDA‘S example5.9. Time substitutio must come from local time integrals5.10. Shunts5.11. Shunts with killing5.12. Creation of mass5.13. A parabolic equation5.f4. Explosio5.15. A non-linear parabolic equationChapter 6. Local and invee local times6.1. Local and invee local times6.2. LEVY measures6.3. t and the intervals of [0， + ∞）6.4. A counter example： t and the intervals of [0， +∞）6.5a t and downcrossings6.5b t as HAUSDORFF measure6.5c t as diffusion6.5d Excuio6.6. Dimeion numbe6.7. Comparison tests Noteion Dimeion numbe and fractional dimeional capacities6.8. An individual ergodic theoremChapter 7. BRowNian motion in several dimeio7.1. Diffusion in several dimeio7.2. The standard BRowNian motion in several dimeio7.3. Wandering out to oo7.4. GREENian domai and GREEN functio7.5. Excessive functio7.6. Application to the spectrum of /1/27.7. Potentials and hitting probabilities7.8. NEWTONian capacities7.9. GAUSS’s quadratic form7.10. WIENER‘S test7.11. Applicatio of WIENER’S test7.12. DIRICHLET problem7.13. NEUHANN problem7.14. Space-time BROWNian moticn7.15. Spherical BROWNian motion and skew products7.16. Spinning7.17. An individual ergodic theorem for the standard 2-dimeional BROWNian motion7.18. Covering BROWNian motio7.19. Diffusio with BROWNian hitting probabilities7.20. Right-continuous paths7.21. RIESZ potentialsChapter 8. A general view of diffusion in several dimeio8.1. Similar diffusio8.2. as differential operater8.3. Time substitutio8.4. Potentials8.5. Boundaries8.6. Elliptic operato8.7. FELLER‘S little boundary and tail algebrasBibliographyList of notatioIndex
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英文影印对我来说主要作用在装门面，，，
这是好书。由伊藤先生亲自撰写的质量当然没得说。但这本书写于上世纪70年代。有些数学符号和文字叙述与现在有不小区别，且其内容本身就需要研究生水平的人才能阅读，导致阅读起来难度很大。