The subject of this book is stochastic partial differential equations, in particular, reaction-diffusion equations, Burgers and Navier-Stokes equations and the corresponding Kolmogorov equations. For each case the transition semigroup is considered and irreducibility, the strong Feller property, and invariant measures are investigated. Moreover, it is proved that the exponential functions provide a core for the infinitesimal generator. As a consequence, it is possible to study Sobolev spaces with respect to invariant measures and to prove a basic formula of integration by parts (the so-called 'carré du champs identity'. Several results were proved by the author and his collaborators and appear in book form for the first time. Presenting the basic elements of the theory in a simple and compact way, the book covers a one-year course directed to graduate students in mathematics or physics. The only prerequisites are basic probability (including finite dimensional stochastic differential equations), basic functional analysis and some elements of the theory of partial differential equations.
Auflage
Sprache
Verlagsort
Verlagsgruppe
Kluwer Academic Publishers Group
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Illustrationen
Maße
Höhe: 241 mm
Breite: 160 mm
Dicke: 21 mm
Gewicht
ISBN-13
978-0-306-41802-0 (9780306418020)
DOI
10.1007/978-1-4899-1831-4
Schweitzer Klassifikation
Recent Advances in Interpenetrating Polymer Networks.- Adhesion between Polymers.- Principles and Technologies of Polymer Blending.- The Role of Interfacial Agents in Polymer Blends.- Morphology, Crystallization and Melting Behaviour of Thin Films of Isotactic Polypropylene Blended with Several Rubbers.- Properties of Poly(Ethylene Oxide) / Poly(Methylmethacrylate) Blends: Morphology, Crystallization and Melting Behaviour.- Suspension Model for Elastic Modulus of Two-Component Polymer Blends.- Compatibility of PVC-Polymethacrylate Systems.- Linear Polyethylene/Polypropylene/Ethylene-Propylene Copolymer Ternary Blends: I. Relationship Between Impact Properties and Morphology.- Linear Polyethylene/Polypropylene/Ethylene-Propylene Copolymer Ternary Blends: II. Relationship Between Mechanical Properties and Morphology.- Formation of EDA Complexes in Polymer Mixtures.- Electrical Properties of Polypropylyne-Polycarbonate Blends.- New Conductive Polymeric Composites.- Anisotropy of Electrical Conductivity in Films of Polycarbonate with CT Complex Obtained by Zone Solidification.- The Influence of Interfacial Grafting on the Properties of Elastomer - Plastomer Mixtures.- Synthesis and Characterization of Interfacial Agents to be used in Polyamide 6/Rubber Blends.- A Mechanical Study of Polyethylene-Glass Beads Adhesion.- The Structure and Tensile Properties of Cold Drawn Modified Chalk Filled Polypropylene.- Composite Membranes Containing Liquid Crystals - Some Thermal and Mechanical Properties.- Structure and Properties of Two-Component Membranes Made of Ionic/Nonionic Polymers with Gradient Content of an Ionic Component.- "Multicomponent" Segmented Polyester Systems Containing Mesogenic Residues.
