Stochastic Partial Differential Equations
11%
off

Stochastic Partial Differential Equations

4 (1 rating by Goodreads)
By (author) 

Free delivery worldwide

Available. Dispatched from the UK in 3 business days
When will my order arrive?

Description

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theory and Ito's equations, highlighting several computational and analytical techniques.

Without assuming specific knowledge of PDEs, the text includes many challenging problems in stochastic analysis and treats stochastic PDEs in a practical way. The author first brings the subject back to its root in classical concrete problems. He then discusses a unified theory of stochastic evolution equations and describes a few applied problems, including the random vibration of a nonlinear elastic beam and invariant measures for stochastic Navier-Stokes equations. The book concludes by pointing out the connection of stochastic PDEs to infinite-dimensional stochastic analysis.

By thoroughly covering the concepts and applications of stochastic PDEs at an introductory level, this text provides a guide to current research topics and lays the groundwork for further study.
show more

Product details

  • Hardback | 281 pages
  • 157.5 x 238.8 x 20.3mm | 544.32g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 500 equations; 30 Illustrations, black and white
  • 1584884436
  • 9781584884439
  • 2,578,224

Table of contents

PREFACE

PRELIMINARIES
Introduction
Some Examples
Brownian Motions and Martingales
Stochastic Integrals
Stochastic Differential Equations
Comments

SCALAR EQUATIONS OF FIRST ORDER
Introduction
Generalized Ito's Formula
Linear Stochastic Equations
Quasilinear Equations
General Remarks

STOCHASTIC PARABOLIC EQUATIONS
Introduction
Preliminaries
Solution of Random Heat Equation
Linear Equations with Additive Noise
Some Regularity Properties
Random Reaction-Diffusion Equations
Parabolic Equations with Gradient-Dependent Noise

STOCHASTIC PARABOLIC EQUATIONS IN THE WHOLE SPACE
Introduction
Preliminaries
Linear and Similinear Equations
Feynman-Kac Formula
Positivity of Solutions
Correlation Functions of Solutions

STOCHASTIC HYPERBOLIC EQUATIONS
Introduction
Preliminaries
Wave Equation with Additive Noise
Semilinear Wave Equations
Wave Equations in Unbounded Domain
Randomly Perturbed Hyperbolic Systems

STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES
Introduction
Hilbert Space-Valued Martingales
Stochastic Integrals in Hilbert Spaces
Ito's Formula
Stochastic Evolution Equations
Mild Solutions
Strong Solutions
Stochastic Evolution Equations of Second Order

ASYMPTOTIC BEHAVIOR OF SOLUTIONS
Introduction
Ito's Formula and Lyapunov Functionals
Boundedness of Solutions
Stability of Null Solution
Invariant Measures
Small Random Perturbation Problems
Large Deviations Problems

FURTHER APPLICATIONS
Introduction
Stochastic Burgers and Related Equations
Random Schroedinger Equation
Nonlinear Stochastic Beam Equations
Stochastic Stability of Cahn-Hilliard Equation
Invariant Measures for Stochastic Navier-Stokes Equations

DIFFUSION EQUATIONS IN INFINITE DIMENSIONS
Introduction
Diffusion Processes and Kolmogorov Equations
Gauss-Sobolev Spaces
Ornstein-Uhlenbeck Semigroup
Parabolic Equations and Related Elliptic Problems
Characteristic Functionals and Hopf Equations

REFERENCES

INDEX
show more

About Pao-Liu Chow

Wayne State University, Detroit, Michigan, USA
show more

Rating details

1 ratings
4 out of 5 stars
5 0% (0)
4 100% (1)
3 0% (0)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X