Probability and Its Applications

Stochastic Differential Equations in Infinite Dimensions

with Applications to Stochastic Partial Differential Equations

Authors: Gawarecki, Leszek, Mandrekar, Vidyadhar

  • Offers comprehensive coverage of modern techniques used for solving problems in infinite dimensional stochastic differential equations
  • Presents major methods, including compactness, coercivity, monotonicity, in different set-ups
  • Provides a broad range of new results and applications
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  • ISBN 978-3-642-16194-0
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  • ISBN 978-3-642-16193-3
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  • ISBN 978-3-642-26634-8
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About this Textbook

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.

Reviews

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)


Table of contents (7 chapters)

  • Partial Differential Equations as Equations in Infinite Dimensions

    Gawarecki, Leszek (et al.)

    Pages 3-16

  • Stochastic Calculus

    Gawarecki, Leszek (et al.)

    Pages 17-72

  • Stochastic Differential Equations

    Gawarecki, Leszek (et al.)

    Pages 73-149

  • Solutions by Variational Method

    Gawarecki, Leszek (et al.)

    Pages 151-184

  • Stochastic Differential Equations with Discontinuous Drift

    Gawarecki, Leszek (et al.)

    Pages 185-200

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-16194-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-3-642-16193-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.95
price for USA
  • ISBN 978-3-642-26634-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Differential Equations in Infinite Dimensions
Book Subtitle
with Applications to Stochastic Partial Differential Equations
Authors
Series Title
Probability and Its Applications
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-16194-0
DOI
10.1007/978-3-642-16194-0
Hardcover ISBN
978-3-642-16193-3
Softcover ISBN
978-3-642-26634-8
Series ISSN
1431-7028
Edition Number
1
Number of Pages
XVI, 291
Topics