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1.

図書
図書
1. Le mouvement brownien relativiste (: Berlin ; : New York)
Jean-Pierre Caubet
出版情報: Berlin ; New York : Springer-Verlag, 1976  ix, 212 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 559
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2.

図書
図書
2. Brownian motion and stochastic flow systems. 1st ed.
J. Michael Harrison
出版情報: New York : Wiley, c1985  xxi, 140 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Applied probability and statistics
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3.

図書
図書
3. Brownian motion, obstacles and random media (: softcover)
Alain-Sol Sznitman
出版情報: Berlin : Springer, c1998  xvi, 353 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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4.

図書
図書
4. Methods of mathematical finance
Ioannis Karatzas, Steven E. Shreve
出版情報: New York : Springer, c1998  xv, 407 p. ; 24 cm
シリーズ名: Applications of mathematics ; 39
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目次情報: 続きを見る
A Brownian Motion of Financial Markets
Contingent Claim Valuation in a Complete Market
Single-Agent Consumption and Investment
Equilibrium in a Complete Market
Contingent Claims in Incomplete Markets
Constrained Consumption and Investment
A Brownian Motion of Financial Markets
Contingent Claim Valuation in a Complete Market
Single-Agent Consumption and Investment
5.

図書
図書
5. Continuous martingales and Brownian motion. 3rd ed
Daniel Revuz, Marc Yor
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1999  xiii, 602 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 293
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6.

図書
図書
6. Brownian motion and index formulas for the de Rham complex
Kazuaki Taira
出版情報: Berlin : Wiley-VCH, c1998  215 p. ; 24 cm
シリーズ名: Mathematical research ; vol. 106
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7.

図書
図書
7. From Brownian motion to Schrödinger's equation (: gw ; : us)
Kai Lai Chung, Zhongxin Zhao
出版情報: Berlin ; New York : Springer-Verlag, c1995  xii, 287 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 312
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目次情報: 続きを見る
Preparatory Material / 1：
Basic Notation / 1.1：
Markov Process and Strong Markov Property / 1.2：
Construction of Brownian Motion / 1.3：
Harmonic Function and Poisson Kernel / 1.4：
Exit Time and Place / 1.5：
Dirichlet Boundary Value Problem / 1.6：
Appendix to Chapter 1
Notes on Chapter 1
Killed Brownian Motion / 2：
Feller Properties / 2.1：
Transition Density / 2.2：
Green Potential and Function / 2.3：
Compactness and Spectrum / 2.4：
Laplacian as Generator / 2.5：
Notes on Chapter 2
Schrodinger Operator / 3：
The Schrodinger Equation and Class J / 3.1：
Semigroup with Multiplicative Functional / 3.2：
Potential Operator and its Inverse / 3.3：
Schrodinger Infinitesimal Generator / 3.4：
Notes on Chapter 3
Stopped Feynman-Kac Functional / 4：
Harnack Inequality and Gauge Theorem / 4.1：
Fundamental Properties of the Gauge / 4.2：
Dirichlet Boundary Value Problem for the Schrodinger Equation / 4.4：
Representation Theorem / 4.5：
Equivalence Theorem for Gaugeability / 4.6：
Notes on Chapter 4
Conditional Brownian Motion and Conditional Gauge / 5：
Conditional Brownian Motion / 5.1：
Life in a Lipschitz Domain / 5.2：
Conditional Gauge for a Small Ball / 5.3：
General Gauge Theorem / 5.4：
Continuity of Weak Solutions / 5.5：
New Approach to the Gauge Theorem / 5.6：
Notes on Chapter 5
Green Functions / 6：
Basic Properties of the q-Green Function / 6.1：
Notes on Chapter 6 / 6.2：
Conditional Gauge and q-Green Function / 7：
Conditional Gauge Theorem / 7.1：
Approximation and Continuity of the Conditional Gauge / 7.2：
Extended Conditional Gauge Theorem / 7.3：
Representation of the Conditional Gauge / 7.4：
Notes on Chapter 7
Various Related Developments / 8：
Variation of Gauge / 8.1：
Variation of the Principal Eigenvalue / 8.2：
Principal Eigenfunction and Sharp Variation / 8.3：
Boundary Harnack Principle and Application / 8.4：
Schrodinger Equation in the Classical Setting / 8.5：
Dirichlet Problem and Truncated Gauge / 8.6：
Notes on Chapter 8
The Case of One Dimension / 9：
Fundamental Expectations / 9.1：
Gauge for a Finite or Infinite Interval / 9.2：
Special Cases and Examples / 9.3：
Local Time and Density / 9.4：
Derivatives and Neumann's Problem / 9.5：
Notes on Chapter 9
References
Index
Preparatory Material / 1：
Basic Notation / 1.1：
Markov Process and Strong Markov Property / 1.2：
8.

図書
図書
8. Probabilities on the Heisenberg group : limit theorems and Brownian motion
Daniel Neuenschwander
出版情報: Berlin : Springer, c1996  viii, 139 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1630
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9.

図書
図書
9. Handbook of Brownian motion : facts and formulae (: Basel ; : Boston)
Andrei N. Borodin, Paavo Salminen
出版情報: Basel : Birkhäuser, c1996  xiv, 462 p. ; 24 cm
シリーズ名: Probability and its applications
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10.

図書
図書
10. Lectures from Markov processes to Brownian motion (: us ; : gw)
Kai Lai Chung
出版情報: New York ; Berlin : Springer-Verlag, c1982  viii, 239 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 249
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11.

図書
図書
11. Random walks, Brownian motion and interacting particle systems : a festschrift in honor of Frank Spitzer (: us ; : gw)
Rick Durrett, Harry Kesten, editors
出版情報: Boston : Birkhäuser, 1991  ix, 455 p. ; 24 cm
シリーズ名: Progress in probability ; 28
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12.

図書
図書
12. Some special functionals (: sz ; : us)
Marc Yor
出版情報: Basel ; Boston : Birkhäuser, 1992  136 p. ; 25 cm
シリーズ名: Lectures in mathematics ETH Zürich ; . Some aspects of Brownian motion ; part. 1
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13.

図書
図書
13. Brownian motion and diffusion
David Freedman
出版情報: San Francisco : Holden-Day, c1971  xii, 231 p ; 24 cm
シリーズ名: Holden-Day series in probability and statistics
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14.

図書
図書
14. Brownian motion (: us ; : gw)
T. Hida ; translated by the author and T.P. Speed
出版情報: New York : Springer-Verlag, c1980  xvi, 325 p. ; 25 cm
シリーズ名: Applications of mathematics ; 11
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15.

図書
図書
15. Essentials of Brownian motion and diffusion
by Frank B. Knight
出版情報: Providence, R.I. : American Mathematical Society, 1981  xiii, 201 p. ; 27 cm
シリーズ名: Mathematical surveys ; no. 18
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16.

図書
図書
16. Brownian motion and stochastic calculus (: U.S. ; : Germany)
Ioannis Karatzas, Steven E. Shreve
出版情報: New York ; Tokyo : Springer-Verlag, c1988  xxiii, 470 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 113
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17.

図書
図書
17. Continuous martingales and Brownian motion. 2nd ed (: gw ; : us)
Daniel Revuz, Marc Yor
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1994  xi, 560 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 293
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18.

図書
図書
18. 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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目次情報: 続きを見る
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：
19.

図書
図書
19. Handbook of Brownian motion : facts and formulae. 2nd ed.
Andrei N. Borodin, Paavo Salminen
出版情報: Basel : Birkhäuser, c2002  xv, 672 p. ; 24 cm
シリーズ名: Probability and its applications
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20.

図書
図書
20. Exponential functionals of Brownian motion and related processes
Marc Yor
出版情報: Berlin : Springer, c2001  vii, 203 p. ; 24 cm
シリーズ名: Springer finance
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目次情報: 続きを見る
On certain exponential functions of real Brownian motion
On Some Exponential Functionals of Brownian Motion
Some relations between Bessel processes
Asian options and confluent hypergeometric functions
The laws of exponential functions of Brownian motion, taken at various random times
Bessel Processes
Asian option and perpetuities
Further Results on Exponential Functionals of Brownian Motion
From Planar Brownian Windings to Asian Options
On exponential functions of certain Levy processes
On Some Exponential-Integral Functionals of Bessel Processes
Exponential Functionals of Brownian Motion and Disordered Systems
On certain exponential functions of real Brownian motion
On Some Exponential Functionals of Brownian Motion
Some relations between Bessel processes
21.

電子ブック
ＥＢ
21. Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes (: electronic bk)
N.U. Ahmed
出版情報: [Singapore] : World Scientific, [20--]  1 online resource (xiv, 299 p.)
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目次情報: 続きを見る
Preface
Background Material / 1：
Introduction / 1.1：
Wiener Process and Wiener Measure / 1.2：
Stochastic Differential Equations in Rd / 1.3：
Stochastic Differential Equations in H / 1.4：
Measure Solutions / 1.4.1：
Nonlinear Filtering / 1.5：
Finite Dimensional Filtering / 1.5.1：
Infinite Dimensional Filtering / 1.5.2：
Elements of Vector Measures / 1.6：
Some Problems for Exercise / 1.7：
Regular Functionals of Brownian Motion / 2：
Functionals of Scalar Brownian Motion / 2.1：
Functionals of Vector Brownian Motion / 2.3：
Functionals of Gaussian Random Field (GRF) / 2.4：
Functionals of Multidimensional Gaussian Random Fields / 2.5：
Functionals of co-Dimensional Brownian Motion / 2.6：
Fr-Br. Motion and Regular Functionals Thereof / 2.7：
Levy Process and Regular Functionals Thereof / 2.8：
Generalized Functionals of the First Kind I / 2.9：
Mild Generalized Functionals I / 3.1：
Mild Generalized Functionals II / 3.3：
Generalized Functionals of GRF I / 3.4：
Generalized Functionals of GRF II / 3.5：
Generalized Functionals of co-Dim. Brownian Motion / 3.6：
Generalized Functionals of Fr.Brownian Motion and Levy Process / 3.7：
Functional Analysis on {G, g} and Their Duals / 3.8：
Compact and Weakly Compact Sets / 4.1：
Some Optimization Problems / 4.3：
Applications to SDE / 4.4：
Vector Measures / 4.5：
Application to Nonlinear Filtering / 4.6：
Application to Infinite Dimensional Systems / 4.7：
Levy Optimization Problem / 4.8：
I2-Based Generalized Functionals of White Noise II / 4.9：
Characteristic Function of White Noise / 5.1：
Multiple Wiener-Ito Integrals / 5.3：
Generalized Hida-Functionals / 5.4：
Application to Quantum Mechanics / 5.5：
Lp-Based Generalized Functionals of White Noise III / 5.6：
Homogeneous Functionals of Degree n / 6.1：
Nonhomogeneous Functionals / 6.3：
Weighted Generalized Functionals / 6.4：
Some Examples Related to Section 6.4 / 6.5：
Generalized Functionals of Random Fields Applied / 6.6：
Fq-Valued Vector Measures with Application / 6.7：
Wpm Based Generalized Functionals of White Noise IV / 6.8：
Homogeneous Functionals / 7.1：
Inductive and Projective Limits / 7.3：
Abstract Generalized Functionals / 7.5：
Vector Measures with Values from Wiener-Ito Distributions / 7.6：
Application to Stochastic Navier-Stokes Equation / 7.7：
Some Elements of Malliavin Calculus / 7.9：
Abstract Wiener Space / 8.1：
Malliavin Derivative and Integration by Parts / 8.3：
Operator d the Adjoint of the Operator D / 8.4：
Ornstein-Uhlenbeck Operator L / 8.5：
Sobolev Spaces on Wiener Measure Space fi = (fi,/i) / 8.6：
Smoothness of Probability Measures / 8.7：
Smoothness under Ellipticity Condition / 8.7.1：
Smoothness under Horrnander's Conditions / 8.7.2：
Some Illustrative Examples / 8.7.3：
Some Comments on Degeneracy Condition / 8.7.4：
Central Limit Theorem for Wiener-Ito Functionals / 8.8：
Malliavin Calculus for Fr-Brownian Motion / 8.9：
Evolution Equations on Fock Spaces / 8.10：
Malliavin Operators on Fock Spaces / 9.1：
Evolution Equations on Abstract Fock Spaces / 9.3：
Evolution Equations Determined by Coercive Operators on Fock Spaces / 9.4：
An Example / 9.5：
Evolution Equations on Wiener-Sobolev Spaces / 9.6：
Some Examples for Exercise / 9.7：
Bibliography
Index
Preface
Background Material / 1：
Introduction / 1.1：
22.

電子ブック
ＥＢ
22. 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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目次情報: 続きを見る
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
23.

電子ブック
ＥＢ
23. Microhydrodynamics, Brownian Motion, and complex fluids (: electronic bk)
Michael D. Graham
出版情報:   1 online resource (xiv, 266 p.)
シリーズ名: Cambridge texts in applied mathematics ; 58
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24.

図書
図書
24. Continuous Martingales and Brownian motion (: gw ; : us)
Daniel Revuz, Marc Yor
出版情報: Berlin ; Tokyo : Springer-Verlag, c1991  ix, 533 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 293
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25.

図書
図書
25. Brownian motion and stochastic calculus. 2nd ed (: us ; : gw)
Ioannis Karatzas, Steven E. Shreve
出版情報: New York ; Tokyo : Springer-Verlag, c1991  xxiii, 470 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 113
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目次情報: 続きを見る
Martingales, Stopping Times, and Filtrations
Brownian Motion
Stochastic Integration
Brownian Motion and Partial Differential Equations
Stochastic Differential Equations
LFvy's Theory of Brownian Local Time
Martingales, Stopping Times, and Filtrations
Brownian Motion
Stochastic Integration
26.

図書
図書
26. Some recent martingale problems (: sz ; : us)
Marc Yor
出版情報: Basel ; Boston : Birkhäuser, c1997  xii, 144 p. ; 24 cm
シリーズ名: Lectures in mathematics ETH Zürich ; . Some aspects of Brownian motion / Marc Yor ; pt. 2
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