Stochastic Partial Differential Equations
Auteur : Chow Pao-Liu
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 Itô'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.
Date de parution : 11-2019
15.6x23.4 cm
Date de parution : 03-2007
Ouvrage de 320 p.
15.6x23.4 cm
Thèmes de Stochastic Partial Differential Equations :
Mots-clés :
Stochastic Reaction Diffusion Equation; Ordinary Differential Equations; evolution; Stochastic Transport Equation; wiener; Stochastic Evolution Equations; process; Stochastic Ordinary Differential Equations; invariant; Stochastic Parabolic Equation; measure; Stratonovich Integral; hilbert; Mild Solution; space; Lyapunov Functional; cauchy; Cauchy Problem; problem; Continuous Semimartingale; random; Stochastic Integral; stochastic parabolic equations; Unique Strong Solution; Linear Parabolic Equation; Random Field; Fourier transform; Stochastic Integral Equation; infinite-dimensional stochastic analysis; Null Solution; Local Martingale; Stochastic Flow; Exponentially Stable; Unique Invariant Measure; Parabolic Equation; Feller Property; Large Deviations Principle; Multiplicative White Noise