Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The aim of this book is to give a systematic and self-contained presentation of the basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by It and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof.

Stochastic partial differential equations --- Stochastic partial differential equations. --- Stochastic processes --- Équations aux dérivées partielles stochastiques

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

Mathematics. --- Partial differential equations. --- Probabilities. --- Fluids. --- Probability Theory and Stochastic Processes. --- Partial Differential Equations. --- Fluid- and Aerodynamics. --- Probability --- Statistical inference --- Partial differential equations --- Math --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Science --- Distribution (Probability theory. --- Differential equations, partial. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Stochastic processes. --- Random processes