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Stochastic Differential Equations in Infinite Dimensions

with Applications to Stochastic Partial Differential Equations

Leszek Gawarecki, Vidyadhar Mandrekar (Autoren)

Buch | Hardcover

XVI, 291 Seiten

2010 | 2011
Springer Berlin (Verlag)
978-3-642-16193-3 (ISBN)

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The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance.Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included.This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE's. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.

Preface.- Part I: Stochastic Differential Equations in Infinite Dimensions.- 1.Partial Differential Equations as Equations in Infinite.- 2.Stochastic Calculus.- 3.Stochastic Differential Equations.- 4.Solutions by Variational Method.- 5.Stochastic Differential Equations with Discontinuous Drift.- Part II: Stability, Boundedness, and Invariant Measures.- 6.Stability Theory for Strong and Mild Solutions.- 7.Ultimate Boundedness and Invariant Measure.- References.- Index.

From the reviews:

"The text is complete, accurate and a very clear introduction to the topic. ... the book is a very nice and clear introduction to major methods in the study of infinite-dimensional stochastic differential equations. The book is not only appropriate for teaching purposes (it is designed for graduate students but due to its clear approach it can probably be used in undergraduate classes as well), but also a robust reference work for pure and applied mathematicians." (Giorgio Fabbri, Mathematical Reviews, Issue 2012 a)

Erscheint lt. Verlag	15.12.2010
Reihe/Serie	Probability and Its Applications
Zusatzinfo	XVI, 291 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	595 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	35-XX, 60-XX • infinite dimensions • Infinitesimalrechnung • Partial differential equations • Quantitative Finance • Stochastic differential equations • Stochastische Differenzialgleichungen
ISBN-10	3-642-16193-6 / 3642161936
ISBN-13	978-3-642-16193-3 / 9783642161933
Zustand	Neuware