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図書
図書
1. Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction
Horst Osswald
出版情報: Cambridge : Cambridge University Press, 2012  xix, 407 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 191
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The Fundamental Principles / Part I：
Preface / 1：
Martingales / 2：
Fourier and Laplace transformations / 3：
Abstract Wiener-Fréchet spaces / 4：
Two concepts of no-anticipation in time / 5：
Malliavin calculus on the space of real sequences / 6：
Introduction to poly-saturated models of mathematics / 7：
Extension of the real numbers and properties / 8：
Topology / 9：
Measure and integration on Loeb spaces / 10：
An Introduction to Finite- and Infinite-Dimensional Stochastic Analysis / Part II：
From finite- to infinite-dimensional Brownian motion / 11：
The Itô integral for infinite-dimensional Brownian motion / 12：
The iterated integral / 13：
Infinite-dimensional Ornstein-Uhlenbeck processes / 14：
Lindstrøm's construction of standard Lévy processes from discrete ones / 15：
Stochastic integration for Lévy processes / 16：
Malliavin Calculus / Part III：
Chaos decomposition / 17：
The Malliavin derivative / 18：
The Skorokhod integral / 19：
The interplay between derivative and integral / 20：
Skorokhod integral processes / 21：
Girsanov transformation / 22：
Malliavin calculus for Lévy processes / 23：
Poly-saturated models / Appendix A：
The existence of poly-saturated models / Appendix B：
References
Index
The Fundamental Principles / Part I：
Preface / 1：
Martingales / 2：
2.

電子ブック
ＥＢ
2. Brownian motion (: electronic bk)
Peter Mörters and Yuval Peres ; with an appendix by Oded Schramm and Wendelin Werner
出版情報: [Cambridge] : Cambridge University Press, 2012  1 online resource (xii, 403 p.)
シリーズ名: Cambridge series on statistical and probabilistic mathematics
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Preface
Frequently used notation
Motivation
Brownian motion as a random function / 1：
Paul Lévy's construction of Brownian motion / 1.1：
Continuity properties of Brownian motion / 1.2：
Nondifferentiability of Brownian motion / 1.3：
The Cameron-Martin theorem / 1.4：
Exercises
Notes and comments
Brownian motion as a strong Markov process / 2：
The Markov property and Blumenthal's 0-1 law / 2.1：
The strong Markov property and the reflection principle / 2.2：
Markov processes derived from Brownian motion / 2.3：
The martingale property of Brownian motion / 2.4：
Harmonic functions, transience and recurrence / 3：
Harmonic functions and the Dirichlet problem / 3.1：
Recurrence and transience of Brownian motion / 3.2：
Occupation measures and Green's functions / 3.3：
The harmonic measure / 3.4：
Hausdorff dimension: Techniques and applications / 4：
Minkowski and Hausdorff dimension / 4.1：
The mass distribution principle / 4.2：
The energy method / 4.3：
Frostman's lemma and capacity / 4.4：
Brownian motion and random walk / 5：
The law of the iterated logarithm / 5.1：
Points of increase for random walk and Brownian motion / 5.2：
Skorokhod embedding and Donsker's invariance principle / 5.3：
The arcsine laws for random walk and Brownian motion / 5.4：
Pitman's 2M - B theorem / 5.5：
Brownian local time / 6：
The local time at zero / 6.1：
A random walk approach to the local time process / 6.2：
The Ray-Knight theorem / 6.3：
Brownian local time as a Hausdorff measure / 6.4：
Stochastic integrals and applications / 7：
Stochastic integrals with respect to Brownian motion / 7.1：
Conformal invariance and winding numbers / 7.2：
Tanaka's formula and Brownian local time / 7.3：
Feynman-Kac formulas and applications / 7.4：
Potential theory of Brownian motion / 8：
The Dirichlet problem revisited / 8.1：
The equilibrium measure / 8.2：
Polar sets and capacities / 8.3：
Wiener's test of regularity / 8.4：
Intersections and self-intersections of Brownian paths / 9：
Intersection of paths: Existence and Hausdorff dimension / 9.1：
Intersection equivalence of Brownian motion and percolation limit sets / 9.2：
Multiple points of Brownian paths / 9.3：
Kaufman's dimension doubling theorem / 9.4：
Exceptional sets for Brownian motion / 10：
The fast times of Brownian motion / 10.1：
Packing dimension and limsup fractals / 10.2：
Slow times of Brownian motion / 10.3：
Cone points of planar Brownian motion / 10.4：
Further developments / Appendix A：
Stochastic Loewner evolution and planar Brownian motion / Oded Schramm ; Wendelin Werner11：
Some subsets of planar Brownian paths / 11.1：
Paths of stochastic Loewner evolution / 11.2：
Special properties of SLE(6) / 11.3：
Exponents of stochastic Loewner evolution / 11.4：
Background and prerequisites / Appendix B：
Convergence of distributions / 12.1：
Gaussian random variables / 12.2：
Martingales in discrete time / 12.3：
Trees and flows on trees / 12.4：
Hints and solutions for selected exercises
Selected open problems
Bibliography
Index
Hausdorff dimension: techniques and applications
Stochastic Loewner evolution and its applications to planar Brownian motion
References
Preface
Frequently used notation
Motivation
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