A Minicourse on Stochastic Partial Differential Equations

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A Minicourse on Stochastic Partial Differential Equations / Robert Dalang, Robert C. Dalang, Davar Khoshnevisan, Carl Mueller, David Nualart, Firas Rassoul-Agha, F. Takens, Yimin Xiao, F. Takens, B. Teissier, Davar Khoshnevisan, Firas Rassoul-Agha. edited by J. -M. Morel

資料種別:

電子ブック

出版情報:

SpringerLink Books - AutoHoldings
Springer Berlin Heidelberg, 2009

著者名:

edited by J. -M. Morel, F. Takens, B. Teissier, Davar Khoshnevisan, Firas Rassoul-Agha.

さらに 4 件

ISBN:

9783540859932 [3540859934]
9783540859949 [3540859942]

書誌ID:

OB00485222

子書誌情報

フルテキスト

所蔵情報

書誌詳細

言語:

英語

目次情報:

A Primer on Stochastic Partial Differential Equations / Davar Khoshnevisan

What is an SPDE? / 1：

Gaussian Random Vectors / 2：

Gaussian Processes / 3：

Regularity of Random Processes / 4：

Martingale Measures / 5：

A Nonlinear Heat Equation / 6：

From Chaos to Order / 7：

References

The Stochastic Wave Equation / Robert C. Dalang

Introduction

Spatially Homogeneous Gaussian Noise

The Wave Equation in Spatial Dimension 2

A Function-Valued Stochastic Integral

The Wave Equation in Spatial Dimension d >= 1

Spatial Regularity of the Stochastic Integral (d = 3)

Holder-Continuity in the 3-d Wave Equation / 8：

Application of Malliavin Calculus to Stochastic Partial Differential Equations / David Nualart

Malliavin Calculus

Application of Malliavin Calculus to Regularity of Probability Laws

Stochastic Heat Equation

Spatially Homogeneous SPDEs

Some Tools and Results for Parabolic Stochastic Partial Differential Equations / Carl Mueller

Basic Framework

Duality

Large Deviations for SPDEs

A Comparison Theorem

Applications

Sample Path Properties of Anisotropic Gaussian Random Fields / Yimin Xiao

Examples and General Assumptions

Properties of Strong Local Nondeterminism

Modulus of Continuity

Small Ball Probabilities

Hausdorff and Packing Dimensions of the Range and Graph

Hausdorff Dimension of the Level Sets and Hitting Probabilities

Local Times and Their Joint Continuity

List of Participants

Index

A Primer on Stochastic Partial Differential Equations / Davar Khoshnevisan

What is an SPDE? / 1：

Gaussian Random Vectors / 2：

Gaussian Processes / 3：

Regularity of Random Processes / 4：

Martingale Measures / 5：

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