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Course on rough paths : with an introduction to regularity structures / Peter K. Friz and Martin Hairer.

By: Contributor(s): Material type: TextTextSeries: UniversitextPublication details: Switzerland : Springer, 2014.Description: xiv, 251 p. : illustrations ; 24 cmISBN:
  • 9783319083315
Subject(s): DDC classification:
  • 519.2 23 F921
Contents:
1. Introduction -- 2. The space of rough paths -- 3. Brownian motion as a rough path -- 4. Integration against rough paths -- 5. Stochastic integration and Itô's formula -- 6. Doob-Meyer type decomposition for rough paths -- 7. Operations on controlled rough paths -- 8. Solutions to rough differential equations -- 9. Stochastic differential equations -- 10. Gaussian rough paths -- 11. Cameron-Martin regularity and applications -- 12. Stochastic partial differential equations -- 13. Introduction to regularity structures -- 14. Operations on modelled distributions -- 15. Application to the KPZ equation-- References-- Index.
Summary: This book presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension - the theory of regularity structures - and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 519.2 F921 (Browse shelf(Opens below)) Available 135844
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. The space of rough paths --
3. Brownian motion as a rough path --
4. Integration against rough paths --
5. Stochastic integration and Itô's formula --
6. Doob-Meyer type decomposition for rough paths --
7. Operations on controlled rough paths --
8. Solutions to rough differential equations --
9. Stochastic differential equations --
10. Gaussian rough paths --
11. Cameron-Martin regularity and applications --
12. Stochastic partial differential equations --
13. Introduction to regularity structures --
14. Operations on modelled distributions --
15. Application to the KPZ equation--
References--
Index.

This book presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension - the theory of regularity structures - and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.

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