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1.

図書
図書
1. Stochastic partial differential equations and applications
G. Da Prato and L. Tubaro (editors)
出版情報: Harlow, Essex, England : Longman Scientific & Technical , New York : Copublished in the United States with J. Wiley, 1992  286 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 268
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2.

図書
図書
2. Applications croissantes et équations d'évolutions dans les espaces de Banach
G. da Prato
出版情報: London ; New York : Academic Press, 1976  146 p. ; 24 cm
シリーズ名: Institutiones mathematicae ; vol. 2
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3.

図書
図書
3. Partial differential equation methods in control and shape analysis
edited by Giuseppe Da Prato, Jean-Paul Zolésio
出版情報: New York : Marcel Dekker, c1997  viii, 331 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 188
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4.

図書
図書
4. Stochastic partial differential equations and applications II : proceedings of a conference held in Trento, Italy, February 1-6, 1988 (: gw ; : us)
G. Da Prato, L. Tubaro (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1989  vi, 258 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1390
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5.

図書
図書
5. Second order partial differential equations in Hilbert spaces
Giuseppe Da Prato, Jerzy Zabczyk
出版情報: Cambridge : Cambridge University Press, 2002  xvi, 379 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 293
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目次情報: 続きを見る
Theory in the Space of Continuous Functions / Part I：
Gaussian measures / 1：
Spaces of continuous functions / 2：
Heat equation / 3：
Poisson's equation / 4：
Elliptic equations with variable coefficients / 5：
Ornstein-Uhlenbeck equations / 6：
General parabolic equations / 7：
Parabolic equations in open sets / 8：
Theory in Sobolev Spaces with a Gaussian Measure / Part II：
L2 and Sobolev spaces / 9：
Ornstein-Uhlenbeck semigroups on Lp(H, mu) / 10：
Perturbations of Ornstein-Uhlenbeck semigroups / 11：
Gradient systems / 12：
Applications to Control Theory
Second order Hamilton-Jacobi equations / 13：
Hamilton-Jacobi inclusions / 14：
Theory in the Space of Continuous Functions / Part I：
Gaussian measures / 1：
Spaces of continuous functions / 2：
6.

図書
図書
6. Ergodicity for infinite dimensional systems (: pbk)
G. Da Prato, J. Zabczyk
出版情報: Cambridge ; New York : Cambridge University Press, 1996  xi, 339 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 229
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目次情報: 続きを見る
Markovian Dynamical Systems / Part I：
General dynamical systems / 1：
Canonical Markovian systems / 2：
Ergodic and mixing measures / 3：
Regular Markovian systems / 4：
Invariant Measures For Stochastics For Evolution Equations / Part II：
Stochastic differential equations / 5：
Existence of invariant measures / 6：
Uniqueness of invariant measures / 7：
Densities of invariant measures / 8：
Invariant Measures For Specific Models / Part III：
Ornstein-Uhlenbeck processes / 9：
Stochastic delay systems / 10：
Reaction-diffusion equations / 11：
Spin systems / 12：
Systems perturbed through the boundary / 13：
Burgers equation / 14：
Navier-Stokes equations / 15：
Appendices
Markovian Dynamical Systems / Part I：
General dynamical systems / 1：
Canonical Markovian systems / 2：
7.

図書
図書
7. Stochastic partial differential equations and applications : proceedings of a conference held in Trento, Italy, Sept. 30-Oct. 5, 1985 (: gw ; : us)
edited by G. Da Prato and L. Tubaro
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  257 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1236
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8.

図書
図書
8. Stochastic partial differential equations and applications
edited by Giuseppe Da Prato, Luciano Tubaro
出版情報: New York : M. Dekker, c2002  ix, 460 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 227
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目次情報: 続きを見る
Preface
Contributors
The Semi-Martingale Property of the Square of White Noise Integrators / Luigi Accardi ; Andreas Boukas1.：
SPDEs Leading to Local, Relativistic Quantum Vector Fields with Indefinite Metric and Nontrivial S-Matrix / Sergio Albeverio ; Hanno Gottschalk ; Jiang-Lun Wu2.：
Considerations on the Controllability of Stochastic Linear Heat Equations / Viorel Barbu ; Gianmario Tessitore3.：
Stochastic Differential Equations for Trace-Class Operators and Quantum Continual Measurements / Alberto Barchielli ; Anna Maria Paganoni4.：
Invariant Measures of Diffusion Processes: Regularity, Existence, and Uniqueness Problems / Vladimir I. Bogachev ; Michael Rockner5.：
On the Theory of Random Attractors and Some Open Problems / Tomas Caraballo ; Jose Antonio Langa6.：
Invariant Densities for Stochastic Semilinear Evolution Equations and Related Properties of Transition Semigroups / Anna Chojnowska-Michalik7.：
On Some Generalized Solutions of Stochastic PDEs / Pao-Liu Chow8.：
Riemannian Geometry on the Path Space / A. B. Cruzeiro ; P. Malliavin9.：
A Note on Regularizing Properties of Ornstein-Uhlenbeck Semigroups in Infinite Dimensions / Giuseppe Da Prato ; Marco Fuhrman ; Jerzy Zabczyk10.：
White Noise Approach to Stochastic Partial Differential Equations / T. Deck ; S. Kruse ; J. Potthoff ; H. Watanabe11.：
Some Results on Invariant States for Quantum Markov Semigroups / Franco Fagnola ; Rolando Rebolledo12.：
Stochastic Problems in Fluid Dynamics / Franco Flandoli13.：
Limit Theorems for Random Interface Models of Ginzburg-Landau [down triangle, open open phi] Type / Giambattista Giacomin14.：
Second Order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Optimal Control / Fausto Gozzi15.：
Approximations of Stochastic Partial Differential Equations / Istvan Gyongy16.：
Regularity and Continuity of Solutions to Stochastic Evolution Equations / Anna Karczewska17.：
Some New Results in the Theory of SPDEs in Sobolev Spaces / N. V. Krylov18.：
Lyapunov Function Approaches and Asymptotic Stability of Stochastic Evolution Equations in Hilbert Spaces--A Survey of Recent Developments / Kai Liu ; Aubrey Truman19.：
Strong Feller Infinite-Dimensional Diffusions / Bohdan Maslowski ; Jan Seidler20.：
Optimal Stopping Time and Impulse Control Problems for the Stochastic Navier-Stokes Equations / J. L. Menaldi ; S. S. Sritharan21.：
On Martingale Problem Solutions for Stochastic Navier-Stokes Equation / R. Mikulevicius ; B. Rozovskii22.：
SPDEs Driven by a Homogeneous Wiener Process / Szymon Peszat23.：
Applications of Malliavin Calculus to SPDEs / Marta Sanz-Sole24.：
Stochastic Curvature Driven Flows / Nung Kwan Yip25.：
Preface
Contributors
The Semi-Martingale Property of the Square of White Noise Integrators / Luigi Accardi ; Andreas Boukas1.：
9.

図書
図書
9. An introduction to infinite-dimensional analysis (: pbk)
Giuseppe Da Prato
出版情報: Berlin : Springer, c2006  x, 208 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Gaussian measures in Hilbert spaces / 1：
Notations and preliminaries / 1.1：
One-dimensional Hilbert spaces / 1.2：
Finite dimensional Hilbert spaces / 1.3：
Product probabilities / 1.3.1：
Definition of Gaussian measures / 1.3.2：
Measures in Hilbert spaces / 1.4：
Gaussian measures / 1.5：
Some results on countable product of measures / 1.5.1：
Gaussian random variables / 1.5.2：
Changes of variables involving Gaussian measures / 1.6.1：
Independence / 1.6.2：
The Cameron-Martin space and the white noise mapping / 1.7：
The Cameron-Martin formula / 2：
Introduction and setting of the problem / 2.1：
Equivalence and singularity of product measures / 2.2：
The Feldman-Hajek theorem / 2.3：
Brownian motion / 3：
Construction of a Brownian motion / 3.1：
Total variation of a Brownian motion / 3.2：
Wiener integral / 3.3：
Law of the Brownian motion in L[superscript 2](O, T) / 3.4：
Brownian bridge / 3.4.1：
Multidimensional Brownian motions / 3.5：
Stochastic perturbations of a dynamical system / 4：
Introduction / 4.1：
The Ornstein-Uhlenbeck process / 4.2：
The transition semigroup in the deterministic case / 4.3：
The transition semigroup in the stochastic case / 4.4：
A generalization / 4.5：
Invariant measures for Markov semigroups / 5：
Markov semigroups / 5.1：
Invariant measures / 5.2：
Ergodic averages / 5.3：
The Von Neumann theorem / 5.4：
Ergodicity / 5.5：
Structure of the set of all invariant measures / 5.6：
Weak convergence of measures / 6：
Some additional properties of measures / 6.1：
Positive functionals / 6.2：
The Prokhorov theorem / 6.3：
Existence and uniqueness of invariant measures / 7：
The Krylov-Bogoliubov theorem / 7.1：
Uniqueness of invariant measures / 7.2：
Application to stochastic differential equations / 7.3：
Existence of invariant measures / 7.3.1：
Existence and uniqueness of invariant measures by monotonicity / 7.3.2：
Examples of Markov semigroups / 7.3.3：
The heat semigroup / 8.1：
Initial value problem / 8.2.1：
The Ornstein-Uhlenbeck semigroup / 8.3：
Smoothing property of the Ornstein-Uhlenbeck semigroup / 8.3.1：
L[superscript 2] spaces with respect to a Gaussian measure / 8.3.2：
Notations / 9.1：
Orthonormal basis in L[superscript 2](H, [mu]) / 9.2：
The one-dimensional case / 9.2.1：
The infinite dimensional case / 9.2.2：
Wiener-Ito decomposition / 9.3：
The classical Ornstein-Uhlenbeck semigroup / 9.4：
Sobolev spaces for a Gaussian measure / 10：
Derivatives in the sense of Friedrichs / 10.1：
Some properties of W[superscript 1,2] (H, [mu]) / 10.1.1：
Chain rule / 10.1.2：
Gradient of a product / 10.1.3：
Lipschitz continuous functions / 10.1.4：
Regularity properties of functions of W[superscript 1,2] (H, [mu]) / 10.1.5：
Expansions in Wiener chaos / 10.2：
Compactness of the embedding of W[superscript 1,2] (H, [mu]) in L[superscript 2] (H, [mu]) / 10.2.1：
The adjoint of D / 10.3：
Adjoint operator / 10.3.1：
The adjoint operator of D / 10.3.2：
The Dirichlet form associated to [mu] / 10.4：
Poincare and log-Sobolev inequalities / 10.5：
Hypercontractivity / 10.5.1：
The Sobolev space W[superscript 2,2] (H, [mu]) / 10.6：
Gradient systems / 11：
Assumptions and notations / 11.1：
Moreau-Yosida approximations / 11.1.2：
A motivating example / 11.2：
Random variables in L[superscript 2] (0, 1) / 11.2.1：
The Sobolev space W[superscript 1,2] (H, [nu]) / 11.3：
Symmetry of the operator N[subscript 0] / 11.4：
Some complements on stochastic differential equations / 11.5：
Cylindrical Wiener process and stochastic convolution / 11.5.1：
Stochastic differential equations / 11.5.2：
Self-adjointness of N[subscript 2] / 11.6：
Asymptotic behaviour of P[subscript t] / 11.7：
Compactness of the embedding of W[superscript 1,2] (H, [nu]) in L[superscript 2] (H, [nu]) / 11.7.1：
Linear semigroups theory / A：
Some preliminaries on spectral theory / A.1：
Closed and closable operators / A.1.1：
Strongly continuous semigroups / A.2：
The Hille-Yosida theorem / A.3：
Cores / A.3.1：
Dissipative operators / A.4：
Bibliography
Gaussian measures in Hilbert spaces / 1：
Notations and preliminaries / 1.1：
One-dimensional Hilbert spaces / 1.2：
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