Regularity Theory and Stochastic Flows for Parabolic ISPDES

1. Auflage 1995
ISBN: 978-2-88449-045-0
Verlag: Taylor & Francis Ltd (Sales)

Buch, Englisch, 90 Seiten, Format (B × H): 159 mm x 236 mm, Gewicht: 409 g

The book treats two topics in the theory of stochastic partial differential equations: space-regularity of solutions and existence of stochastic flows. The equations considered in the book are linear parabolic with multiplicative noise, like those arising in non-linear filtering or diffusion models in randomly moving media. Regularity theory in Sobolev spaces is extensively investigated, for homogeneous and non-homogeneous boundary value problems, with a detailed analysis of the new geometrical conditions on coefficients arising as a consequence of the stochaticity. The book provides an account of regularity results that may represent a useful reference for the researcher in stochastic partial differential equations. Regularity theory is then applied to prove the existence of stochastic flows. In spite of the variety of results on stochastic flows obtained by this method, several open problems are pointed out, with the hope of stimulating further research on this subject.

Zielgruppe

Academic and Postgraduate

Autoren/Hrsg.

Flandoli, Franco

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Introduction to the Series, Preface, 1 Introduction, 2 Stochastic Flows: Preliminary Comments, 3 Preliminaries on Well-Posedness and Function Spaces, 4 Regularity in Bounded Domains: Some Counterexamples, 5 Regularity Theory for Homogeneous Problems, 6 Non Homogeneous Boundary Value Problems, 7 Existence and Regularity of Stochastic Flows, 8 An Alternative Approach, Acknowledgements, References, Index

Über Autor(innen)

Franco Flandoli (Universita di Pisa, Italy)