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Stochastic Equations in Infinite Dimensions

- G. Prato, J. Zabczyk
- Mathematics
- 4 February 2008

Preface Introduction Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. Stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with… Expand

Representation and Control of Infinite Dimensional Systems

- A. Bensoussan, M. Delfour, G. Prato, S. Mitter
- Mathematics
- 1992

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… Expand

Representation and Control of Infinite Dimensional Systems, 2nd Edition

- A. Bensoussan, G. Prato, M. Delfour, S. Mitter
- PhysicsSystems and control
- 2007

There is disclosed a charged particle beam apparatus capable of adjusting the convergence angle of the charged particle probe independent of the current in the probe. The apparatus comprises a… Expand

Second order partial differential equations in Hilbert spaces

- G. Prato, J. Zabczyk
- Mathematics
- 25 July 2002

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.… Expand

Strong solutions to the stochastic quantization equations

- G. Prato, A. Debussche
- Mathematics
- 1 October 2003

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… Expand

An Introduction to Infinite-Dimensional Analysis

- G. Prato
- Mathematics
- 28 July 2006

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… Expand

Kolmogorov Equations For Stochastic Pdes

- G. Prato
- Mathematics
- 2004

1 Introduction and Preliminaries.- 1.1 Introduction.- 1.2 Preliminaries ix.- 1.2.1 Some functional spaces.- 1.2.2 Exponential functions.- 1.2.3 Gaussian measures.- 1.2.4 Sobolev spaces W1,2 (H, ?)… Expand

Fully nonlinear stochastic partial differential equations

The authors study a class of fully nonlinear stochastic partial differential equations by the reduction to a family of deterministic fully nonlinear equations using the stochastic characteristic… Expand

Two-Dimensional Navier--Stokes Equations Driven by a Space--Time White Noise

- G. Prato, A. Debussche
- Mathematics
- 1 December 2002

Abstract We study the two-dimensional Navier–Stokes equations with periodic boundary conditions perturbed by a space–time white noise. It is shown that, although the solution is not expected to be… Expand

Ergodicity for the 3D stochastic Navier–Stokes equations

- G. Prato, A. Debussche
- Mathematics
- 1 August 2003

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