擴散過程及其樣本軌道

內(nèi)容概要

　　對與擴散現(xiàn)象有關(guān)的隨機過程產(chǎn)生持久而深刻的影響。不少數(shù)學(xué)家受益于《擴散過程及其樣本軌道(英文版)》一維和多維擴散過程的描述和獨到的布朗運動數(shù)學(xué)見解。傳承這一系列書的風(fēng)格，行文簡潔流暢。每章節(jié)后面都配有問題并有部分解答，很適合作為教材和自學(xué)用書。目次：標準布朗運動；布朗局部時間；一般一維擴散；生成元；局部時間和逆時間序列；多維布朗運動；多維擴散簡述。

書籍目錄

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

圖書封面

圖書標簽Tags

無

評論、評分、閱讀與下載

---

    擴散過程及其樣本軌道 PDF格式下載

---