다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions

https://www.ams.org/bull/1992-27-01/S0273-0979-1992-00266-5/S0273-0979-1992-00266-5.pdf

User’s guide to viscosity solutions of second order partial differential equations

Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

Stochastic Equations in Infinite Dimensions

Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence Theorems.- Uniqueness, Generation of Contraction Semigroups, Error Estimates.- Gradient Flow in the Space of Probability Measures.- Preliminary Results on Measure Theory.- The Optimal Transportation Problem.- The Wasserstein Distance and its Behaviour along Geodesics.- Absolutely Continuous Curves in p(X) and the Continuity Equation.- Convex Functionals in p(X).- Metric Slope and Subdifferential Calculus in (X).- Gradient Flows and Curves of Maximal Slope in p(X).

Gradient Flows: In Metric Spaces and in the Space of Probability Measures

Preface to the Second Edition Preface to Volume I of the First Edition Preface to Volume II of the First Edition List of Figures Introduction Part I. Finite Dimensional Linear Control of Dynamical Systems Control of Linear Finite Dimensional Differential Systems Linear Quadratic Two-Person Zero-Sum Differential Games Part II. Representation of Infinite Dimensional Linear Control Dynamical Systems Semi-groups of Operators and Interpolation Variational Theory of Parabolic Systems Semi-group Methods for Systems with Unbounded Control and Observation Operators Differential Systems with Delays Part III. Qualitative Properties of Linear Control Dynamical Systems Controllability and Observability for a Class of Infinite Dimensional Systems Part IV. Quadratic Optimal Control: Finite Time Horizon Systems with Bounded Control Operators: Control Inside the Domain Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary Part V. Quadratic Optimal Control: Infinite Time Horizon Systems with Bounded Control Operators: Control Inside the Domain Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary Appendix A. An Isomorphism Result References Index

Representation and Control of Infinite Dimensional Systems

Part I. Theory in the Space of Continuous Functions: 1. Gaussian measures 2. Spaces of continuous functions 3. Heat equation 4. Poisson's equation 5. Elliptic equations with variable coefficients 6. Ornstein-Uhlenbeck equations 7. General parabolic equations 8. Parabolic equations in open sets Part II. Theory in Sobolev Spaces with a Gaussian Measure: 9. L2 and Sobolev spaces 10. Ornstein-Uhlenbeck semigroups on Lp(H, mu) 11. Perturbations of Ornstein-Uhlenbeck semigroups 12. Gradient systems Part II. Applications to Control Theory: 13. Second order Hamilton-Jacobi equations 14. Hamilton-Jacobi inclusions.

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Second order partial differential equations in Hilbert spaces

In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension.

Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.

An Introduction to Infinite Dimensional Analysis

We prove the existence and uniqueness of a strong solution of the stochastic quantization equation in dimension 2 for almost all initial data with respect to the invariant measure. The method is based on a fixed point result in suitable Besov spaces.

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Giuseppe Da Prato

Papers

Stochastic Equations in Infinite Dimensions

Representation and Control of Infinite Dimensional Systems

Second order partial differential equations in Hilbert spaces

An Introduction to Infinite Dimensional Analysis

Strong solutions to the stochastic quantization equations