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1.

図書
図書
1. Stochastic differential equations : an introduction with applications. 5th ed (: softcover)
Bernt Øksendal
出版情報: Berlin ; New York ; Tokyo : Springer, c1998  xix, 324 p. ; 24 cm
シリーズ名: Universitext
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2.

図書
図書
2. Stochastic differential equations : an introduction with applications. 3rd ed (: gw ; : us)
Bernt Øksendal
出版情報: Berlin ; Tokyo : Springer, c1992  xiii, 224 p. ; 24 cm
シリーズ名: Universitext
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3.

図書
図書
3. Stochastic analysis and related topics VII : proceedings of the Seventh Silivri workshop
Laurent Decreusefond, Bernt K. Øksendal, Ali Süleyman Üstünel, editors
出版情報: Boston : Birkhäuser, c2001  vi, 249 p. ; 25 cm
シリーズ名: Progress in probability / series editors, Thomas Liggett, Charles Newman, Loren Pitt ; 48
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4.

図書
図書
4. Spaces of analytic functions : seminar held at Kristiansand, Norway, June 9-14, 1975 (: u.s. ; : gw)
edited by O.B. Bekken, B.K. Øksendal and A. Stray
出版情報: Berlin ; New York : Springer-Verlag, 1976  viii, 204 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 512
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5.

図書
図書
5. Stochastic partial differential equations : a modeling, white noise functional approach. 2nd ed (: pbk)
Helge Holden ... [et al.]
出版情報: New York ; London : Springer, c2010  xv, 304 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Preface to the Second Edition
Preface to the First Edition
Introduction / 1：
Modeling by Stochastic Differential Equations / 1.1：
Framework / 2：
White Noise / 2.1：
The 1-Dimensional, d-Parameter Smoothed White Noise / 2.1.1：
The (Smoothed) White Noise Vector / 2.1.2：
The Wiener-Itô Chaos Expansion / 2.2：
Chaos Expansion in Terms of Hermite Polynomials / 2.2.1：
Chaos Expansion in Terms of Multiple Itô Integrals / 2.2.2：
The Hida Stochastic Test Functions and Stochastic Distributions. The Kondratiev Spaces (S)m;N, (S)m;N-? / 2.3：
The Hida Test Function Space (S) and the Hida Distribution Space (S)* / 2.3.1：
Singular White Noise / 2.3.2：
The Wick Product / 2.4：
Some Examples and Counterexamples / 2.4.1：
Wick Multiplication and Hitsuda/Skorohod Integration / 2.5：
The Hermite Transform / 2.6：
The (S)N?,r Spaces and the S-Transform / 2.7：
The Topology of (S)N-1 / 2.8：
The F-Transform and the Wick Product on L1(&mu) / 2.9：
The Wick Product and Translation / 2.10：
Positivity / 2.11：
Applications to Stochastic Ordinary Differential Equations / 3：
Linear Equations / 3.1：
Linear 1-Dimensional Equations / 3.1.1：
Some Remarks on Numerical Simulations / 3.1.2：
Some Linear Multidimensional Equations / 3.1.3：
A Model for Population Growth in a Crowded, Stochastic Environment / 3.2：
The General (S)-1 Solution / 3.2.1：
A Solution in L1(&mu) / 3.2.2：
A Comparison of Model A and Model B / 3.2.3：
A General Existence and Uniqueness Theorem / 3.3：
The Stochastic Volterra Equation / 3.4：
Wick Products Versus Ordinary Products: a Comparison Experiment / 3.5：
Variance Properties / 3.5.1：
Solution and Wick Approximation of Quasilinear SDE / 3.6：
Using White Noise Analysis to Solve General Nonlinear SDEs / 3.7：
Stochastic Partial Differential Equations Driven by Brownian White Noise / 4：
General Remarks / 4.1：
The Stochastic Poisson Equation / 4.2：
The Functional Process Approach / 4.2.1：
The Stochastic Transport Equation / 4.3：
Pollution in a Turbulent Medium / 4.3.1：
The Heat Equation with a Stochastic Potential / 4.3.2：
The Stochastic Schrödinger Equation / 4.4：
L1(&mu)Properties of the Solution / 4.4.1：
The Viscous Burgers Equation with a Stochastic Source / 4.5：
The Stochastic Pressure Equation / 4.6：
The Smoothed Positive Noise Case / 4.6.1：
An Inductive Approximation Procedure / 4.6.2：
The 1-Dimensional Case / 4.6.3：
The Singular Positive Noise Case / 4.6.4：
The Heat Equation in a Stochastic, Anisotropic Medium / 4.7：
A Class of Quasilinear Parabolic SPDEs / 4.8：
SPDEs Driven by Poissonian Noise / 4.9：
Stochastic Partial Differential Equations Driven by Lévy Processes / 5：
The White Noise Probability Space of a Lévy Process (d = 1) / 5.1：
White Noise Theory for a Lévy Process (d = 1) / 5.3：
Chaos Expansion Theorems / 5.3.1：
The Lévy-Hida-Kondratiev Spaces / 5.3.2：
White Noise Theory for a Lévy Field (d ≥ l) / 5.4：
Construction of the Lévy Field / 5.4.1：
Chaos Expansions and Skorohod Integrals (d ≥ 1) / 5.4.2：
Waves in a Region with a Lévy White Noise Force / 5.4.3：
Heat Propagation in a Domain with a Lévy White Noise Potential / 5.7：
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
References
List of frequently used notation and symbols
Index
Preface to the Second Edition
Preface to the First Edition
Introduction / 1：
6.

電子ブック
ＥＢ
6. Stochastic partial differential equations : a modeling, white noise functional approach. 2nd ed (: electronic bk)
Helge Holden ... [et al.]
出版情報: [Ann Arbor, Mich.] : ProQuest Ebook Central, [20--]  1 online resource (xv, 304 p.)
シリーズ名: Universitext
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目次情報: 続きを見る
Preface to the Second Edition
Preface to the First Edition
Introduction / 1：
Modeling by Stochastic Differential Equations / 1.1：
Framework / 2：
White Noise / 2.1：
The 1-Dimensional, d-Parameter Smoothed White Noise / 2.1.1：
The (Smoothed) White Noise Vector / 2.1.2：
The Wiener-Itô Chaos Expansion / 2.2：
Chaos Expansion in Terms of Hermite Polynomials / 2.2.1：
Chaos Expansion in Terms of Multiple Itô Integrals / 2.2.2：
The Hida Stochastic Test Functions and Stochastic Distributions. The Kondratiev Spaces (S)m;N, (S)m;N-? / 2.3：
The Hida Test Function Space (S) and the Hida Distribution Space (S)* / 2.3.1：
Singular White Noise / 2.3.2：
The Wick Product / 2.4：
Some Examples and Counterexamples / 2.4.1：
Wick Multiplication and Hitsuda/Skorohod Integration / 2.5：
The Hermite Transform / 2.6：
The (S)N?,r Spaces and the S-Transform / 2.7：
The Topology of (S)N-1 / 2.8：
The F-Transform and the Wick Product on L1(&mu) / 2.9：
The Wick Product and Translation / 2.10：
Positivity / 2.11：
Applications to Stochastic Ordinary Differential Equations / 3：
Linear Equations / 3.1：
Linear 1-Dimensional Equations / 3.1.1：
Some Remarks on Numerical Simulations / 3.1.2：
Some Linear Multidimensional Equations / 3.1.3：
A Model for Population Growth in a Crowded, Stochastic Environment / 3.2：
The General (S)-1 Solution / 3.2.1：
A Solution in L1(&mu) / 3.2.2：
A Comparison of Model A and Model B / 3.2.3：
A General Existence and Uniqueness Theorem / 3.3：
The Stochastic Volterra Equation / 3.4：
Wick Products Versus Ordinary Products: a Comparison Experiment / 3.5：
Variance Properties / 3.5.1：
Solution and Wick Approximation of Quasilinear SDE / 3.6：
Using White Noise Analysis to Solve General Nonlinear SDEs / 3.7：
Stochastic Partial Differential Equations Driven by Brownian White Noise / 4：
General Remarks / 4.1：
The Stochastic Poisson Equation / 4.2：
The Functional Process Approach / 4.2.1：
The Stochastic Transport Equation / 4.3：
Pollution in a Turbulent Medium / 4.3.1：
The Heat Equation with a Stochastic Potential / 4.3.2：
The Stochastic Schrödinger Equation / 4.4：
L1(&mu)Properties of the Solution / 4.4.1：
The Viscous Burgers Equation with a Stochastic Source / 4.5：
The Stochastic Pressure Equation / 4.6：
The Smoothed Positive Noise Case / 4.6.1：
An Inductive Approximation Procedure / 4.6.2：
The 1-Dimensional Case / 4.6.3：
The Singular Positive Noise Case / 4.6.4：
The Heat Equation in a Stochastic, Anisotropic Medium / 4.7：
A Class of Quasilinear Parabolic SPDEs / 4.8：
SPDEs Driven by Poissonian Noise / 4.9：
Stochastic Partial Differential Equations Driven by Lévy Processes / 5：
The White Noise Probability Space of a Lévy Process (d = 1) / 5.1：
White Noise Theory for a Lévy Process (d = 1) / 5.3：
Chaos Expansion Theorems / 5.3.1：
The Lévy-Hida-Kondratiev Spaces / 5.3.2：
White Noise Theory for a Lévy Field (d ≥ l) / 5.4：
Construction of the Lévy Field / 5.4.1：
Chaos Expansions and Skorohod Integrals (d ≥ 1) / 5.4.2：
Waves in a Region with a Lévy White Noise Force / 5.4.3：
Heat Propagation in a Domain with a Lévy White Noise Potential / 5.7：
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
References
List of frequently used notation and symbols
Index
Preface to the Second Edition
Preface to the First Edition
Introduction / 1：
7.

図書
図書
7. 確率微分方程式 : 入門から応用まで
ベァーント・エクセンダール著 ; 谷口説男訳
出版情報: 東京 : シュプリンガー・フェアラーク東京, 1999.3  xii, 387p ; 22cm
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8.

図書
図書
8. Malliavin calculus for Lévy processes with applications to finance. Corr. 2nd print
Giulia Di Nunno, Bernt Øksendal, Frank Proske
出版情報: Heidelberg : Springer, c2009  xiii, 417 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Introduction
The Continuous Case: Brownian Motion / Part I：
The Wiene-Ito Chaos Expansion / 1：
Iterated Ito Integrals / 1.1：
The Wiener-Ito Chaos Expansion / 1.2：
Exercises / 1.3：
The Skorohod Integral / 2：
Some Basic Properties of the Skorohod Integral / 2.1：
The Skorohod Integral as an Extension of the Ito Integral / 2.3：
Malliavin Derivative via Chaos Expansion / 2.4：
The Malliavin Derivative / 3.1：
Computation and Properties of the Malliavin Derivative / 3.2：
Chain Rules for Malliavin Derivative / 3.2.1：
Malliavin Derivative and Conditional Expectation / 3.2.2：
Malliavin Derivative and Skorohod Integral / 3.3：
Skorohod Integral as Adjoint Operator to the Malliavin Derivative / 3.3.1：
An Integration by Parts Formula and Closability of the Skorohod Integral / 3.3.2：
A Fundamental Theorem of Calculus / 3.3.3：
Integral Representations and the Clark-Ocone Formula / 3.4：
The Clark-Ocone Formula / 4.1：
The Clark-Ocone Formula under Change of Measure / 4.2：
Application to Finance: Portfolio Selection / 4.3：
Application to Sensitivity Analysis and Computation of the "Greeks" in Finance / 4.4：
White Noise, the Wick Product, and Stochastic Integration / 4.5：
White Noise Probability Space / 5.1：
The Wiener-Ito Chaos Expansion Revisited / 5.2：
The Wick Product and the Hermite Transform / 5.3：
Some Basic Properties of the Wick Product / 5.3.1：
Hermite Transform and Characterization Theorem for (S)* / 5.3.2：
The Spaces G and G* / 5.3.3：
The Wick Product in Terms of Iterated Ito Integrals / 5.3.4：
Wick Products and Skorohod Integration / 5.3.5：
The Hida-Malliavin Derivative on the Space [Omega] = S'(R) / 5.4：
A New Definition of the Stochastic Gradient and a Generalized Chain Rule / 6.1：
Calculus of the Hida-Malliavin Derivative and Skorohod Integral / 6.2：
Wick Product vs. Ordinary Product / 6.2.1：
Closability of the Hida-Malliavin Derivative / 6.2.2：
Wick Chain Rule / 6.2.3：
Integration by Parts, Duality Formula, and Skorohod Isometry / 6.2.4：
Conditional Expectation on (S)* / 6.3：
Conditional Expectation on G* / 6.4：
A Generalized Clark-Ocone Theorem / 6.5：
The Donsker Delta Function and Applications / 6.6：
Motivation: An Application of the Donsker Delta Function to Hedging / 7.1：
The Donsker Delta Function / 7.2：
The Multidimensional Case / 7.3：
The Forward Integral and Applications / 7.4：
A Motivating Example / 8.1：
The Forward Integral / 8.2：
Ito Formula for Forward Integrals / 8.3：
Relation Between the forward Integral and Skorohod Integral / 8.4：
Ito Formula for Skorohod Integrals / 8.5：
Application to Insider Trading Modeling / 8.6：
Markets with No Friction / 8.6.1：
Markets with Friction / 8.6.2：
The Discontinuous Case: Pure Jummp Levy Processes / 8.7：
A Short Introduction to Levy Processes / 9：
Basics on Levy Processes / 9.1：
The Ito Formula / 9.2：
The Ito Representation Theorem for Pure Jump Levy Processes / 9.3：
Application to Finance: Replicability / 9.4：
Skorohod Integrals / 9.5：
Definition and Basic Properties / 11.1：
Integration by Parts and Closability of the Skorohod Integral / 12.2：
Fundamental Theorem of Calculus / 12.3.3：
A Combination of Gaussian and Pure Jump Levy Noises / 12.4：
Application of Minimal Variance Hedging with Partial Information / 12.6：
Computation of "Greeks" in the Case of Jump Diffusions / 12.7：
The Barndorff-Nielsen and Shephard Model / 12.7.1：
Malliavin Weights for "Greeks" / 12.7.2：
Levy White Noise and Stochastic Distributions / 12.8：
The White Noise Probability Space / 13.1：
An Alternative Chaos Expansion and the White Noise / 13.2：
The Wick Product / 13.3：
Definition and Properties / 13.3.1：
Wick Product and Skorohod Integral / 13.3.2：
Levy-Hermite Transform / 13.3.3：
Spaces of Smooth and Generalized Random Variables: G and G* / 13.4：
The Malliavin Derivative on G* / 13.5：
A Generalization of the Clark-Ocone Theorem / 13.6：
A Combination of Gaussian and Pure Jump Levy Noises in the White Noise Setting / 13.7：
Generalized Chain Rules for the Malliavin Derivative / 13.8：
The Donsker Delta Function of a Levy Process and Applications / 13.9：
The Donsker Delta Function of a Pure Jump Levy Process / 14.1：
An Explicit Formula for the Donsker Delta Function / 14.2：
Chaos Expansion of Local Time for Levy Processes / 14.3：
Application to Hedging in Incomplete Markets / 14.4：
A Sensitivity Result for Jump Diffusions / 14.5：
A Representation Theorem for Functions of a Class of Jump Diffusions / 14.5.1：
Application: Computation of the "Greeks" / 14.5.2：
Definition of Forward Integral and its Relation with the Skorohod Integral / 14.6：
Ito Formula for Forward and Skorohod Integrals / 15.2：
Applications to Stochastic Control: Partial and Inside Information / 15.3：
The Importance of Information in Portfolio Optimization / 16.1：
Optimal Portfolio Problem under Partial Information / 16.2：
Formalization of the Optimization Problem: General Utility Function / 16.2.1：
Characterization of an Optimal Portfolio Under Partial Information / 16.2.2：
Examples / 16.2.3：
Optimal Portfolio under Partial Information in an Anticipating Environment / 16.3：
The Continuous Case: Logarithmic Utility / 16.3.1：
The Pure Jump Case: Logarithmic Utility / 16.3.2：
A Universal Optimal Consumption Rate for an Insider / 16.4：
Formalization of a General Optimal Consumption Problem / 16.4.1：
Characterization of an Optimal Consumption Rate / 16.4.2：
Optimal Consumption and Portfolio / 16.4.3：
Optimal Portfolio Problem under Inside Information / 16.5：
Characterization of an Optimal Portfolio under Inside Information / 16.5.1：
Examples: General Utility and Enlargement of Filtration / 16.5.3：
Optimal Portfolio Problem under Inside Information: Logarithmic Utility / 16.6：
The Pure Jump Case / 16.6.1：
A Mixed Market Case / 16.6.2：
Examples: Enlargement of Filtration / 16.6.3：
Regularity of Solutions of SDEs Driven by Levy Processes / 16.7：
The General Case / 17.1：
Absolute Continuity of Probability Laws / 17.3：
Existence of Densities / 18.1：
Smooth Densities of Solutions to SDE's Driven by Levy Processes / 18.2：
Malliavin Calculus on the Wiener Space / 18.3：
Preliminary Basic Concepts / A.1：
Wiener Space, Cameron-Martin Space, and Stochastic Derivative / A.2：
Malliavin Derivative via Chaos Expansions / A.3：
Solutions
References
Notation and Symbols
Index
Introduction
The Continuous Case: Brownian Motion / Part I：
The Wiene-Ito Chaos Expansion / 1：
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