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1.

図書

図書
Ali Süleyman Üstünel
出版情報: Berlin ; New York : Springer-Verlag, c1995  x, 93 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1610
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2.

図書

図書
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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3.

図書

図書
H. Korezlioglu, A.S. Ustunel (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  371 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1316 . Institut de Mathématiques, Université de Strasbourg
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4.

図書

図書
H. Korezlioglu, A.S. Ustunel, [editors]
出版情報: Berlin ; Tokyo : Springer-Verlag, c1990  268 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1444
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5.

図書

図書
A. Süleyman Üstünel, Moshe Zakai
出版情報: Berlin : Springer, c2000  xiii, 296 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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目次情報: 続きを見る
Introduction
Some Background Material and Preliminary Results / 1:
The Radon-Nikodym Theorem / 1.1:
Uniform Integrability / 1.2:
Two Measures Associated with a Point Transformation / 1.3:
Kakutani's Dichotomy Theorem / 1.4:
The Structure of Non-negative Continuous Martingales / 1.5:
Notes and References
Transformation of Measure Induced by Adapted Shifts / 2:
The Girsanov Theorem / 2.1:
Integrability Conditions on λt / 2.2:
Transformation of Measure Induced on C0([0, 1]) by Direct Shifts / 2.3:
Transformations of Measure Induced on C0([0, 1]) by Indirect Shifts / 2.4:
The Innovation Theorem / 2.5:
A Dimension-free Extension of Results of the Previous Sections / 2.6:
The Representability of Measures by Shifts / 2.7:
Transformation of Measure Induced by General Shifts / 3:
The Change of Variables Formula for a Small Perturbation of the Identity / 3.1:
H-Regularity of Random Variables / 3.3:
Some Preliminaries / 3.4:
The Change of Variables Formula / 3.5:
A Comparison Between the Formulas Associated with Adapted and Non Adapted Cases / 3.6:
The Sard Inequality / 4:
Introduction and Preliminaries / 4.1:
The Measurability of the Forward Image / 4.2:
The Sard Inequality I / 4.3:
The Sard Inequality II / 4.4:
Some Applications to Absolute Continuity / 4.5:
Transformation of Measure Under Anticipative Flows / 5:
Introduction and Finite Dimensional Flows / 5.1:
Cylindrical Flows / 5.2:
Infinite Dimensional Flows / 5.3:
A Singular Flow on the Classical Wiener Space / 5.4:
Monotone Shifts / 6:
Absolute Continuity of Monotone Shifts-I / 6.1:
Absolute Continuity of Monotone Shifts-II / 6.4:
Shifts of Hammerstein Type / 6.5:
Generalized Radon-Nikodym Derivatives / 7:
The Gλ Class of Wiener functionals and its Composition with Shifts / 7.1:
The Gλ-class of Wiener Functionals / 7.2.1:
The Extendibility of Gλ Functionals / 7.2.2:
A Generahzed R-N Derivative for Gλ Functionals / 7.3:
The Conditioning of Gλ Functionals with Respect to Certain Sub-sigma-fields / 7.4:
Composition of the Rademacher Class of Wiener Functionals with Shifts / 7.5:
The Composition Rules / 7.6:
The Cyhndrical Case / 7.6.1:
Extensions of the Composition Rules / 7.6.2:
Random Rotations / 8:
A Partial Converse to Theorem 8.2.1 / 8.1:
The Invertibility of Tw = w + R{w)h and that of &Rcirc; / 8.4:
Stochastic Calculus of Rotations / 8.5:
A New Derivation and Calculation of E[<$>\delta\eta|{\cal B}<$>] / 8.5.1:
Case of Deterministic R / 8.5.2:
Transformations of Measure Induced by Euclidean Motions of the Wiener Path / 8.6:
The Degree Theorem on Wiener Space / 9:
Measure Theoretic Degree / 9.1:
Applications to Absolute Continuity / 9.3:
Relations with Leray-Schauder Degree / 9.4:
Some Inequalities / A:
Gronwall and Young Inequalities / A.1:
Gronwall Inequality / A.1.1:
Young Inequality / A.1.2:
Some Inequalities for det2(IH + A) / A.2:
An Introduction to Malliavin Calculus / B:
Introduction to Abstract Wiener Space / B.1:
An Introduction to Analysis on Wiener Space / B.2:
Construction of Sobolev Derivatives / B.3:
The Divergence / B.4:
Ornstein-Uhlenbeck Operator and Meyer Inequalities / B.5:
Some Useful Lemmas / B.6:
Local Versus Global Differentiability of Wiener Functionals / B.7:
Exponential Integrability of Wiener Functionals and Poincaré Inequality / B.8:
References
Index
Notations
Introduction
Some Background Material and Preliminary Results / 1:
The Radon-Nikodym Theorem / 1.1:
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