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A Concise Course on Stochastic Partial Differential Equation

Claudia Prévôt Michael Röckner

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Analysis; Partial Differential Equations; Probability Theory and Stochastic Processes

Disponibilidad

Institución detectada	Año de publicación	Navegá	Descargá	Solicitá
No detectada	2007	SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-3-540-70780-6

ISBN electrónico

978-3-540-70781-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

2007

Información sobre derechos de publicación

Cobertura temática

Matemáticas

Tabla de contenidos

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doi: 10.1007/978-3-540-70781-3_1

Motivation, Aims and Examples

These lectures will concentrate on (nonlinear) stochastic partial differential equations (SPDEs) of evolutionary type. All kinds of dynamics with stochastic infuence in nature or man-made complex systems can be modelled by such equations. As we shall see from the examples, at the end of this section the state spaces of their solutions are necessarily infinite dimensional such as spaces of (generalized) functions. In these notes the state spaces, denoted by E , will be mostly separable Hilbert spaces, sometimes separable Banach spaces.

Palabras clave: Evolutionary Type; Noise Term; Separable Hilbert Space; Separable Banach Space; Martingale Measure.

Pp. 1-4

doi: 10.1007/978-3-540-70781-3_2

Stochastic Integral in Hilbert Spaces

This chapter is a slight modification of Chap. 1 in [FK01].

Palabras clave: Hilbert Space; Orthonormal Basis; Elementary Process; Wiener Process; Gaussian Random Variable.

Pp. 5-42

doi: 10.1007/978-3-540-70781-3_3

Stochastic Differential Equations in Finite Dimensions

This chapter is an extended version of [Kry99, Section 1].

Pp. 43-54

doi: 10.1007/978-3-540-70781-3_4

A Class of Stochastic Differential Equations

In this chapter we will present one specific method to solve stochastic differential equations in infinite-dimensional spaces, known as the variational approach . The main criterion for this approach to work is that the coefficients satisfy certain monotonicity assumptions. As the main references for Subsection 4.2 we mention [RRW06] and [KR79], but also one should check the references therein.

Palabras clave: Invariant Measure; Wiener Process; Markov Property; Separable Hilbert Space; Porous Medium Equation.

Pp. 55-103