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  • © 2014

Upper and Lower Bounds for Stochastic Processes

Modern Methods and Classical Problems

Authors:

  • Develops modern methods and in particular the "generic chaining" to bound stochastic processes
  • Gives applications to stable processes, infinitely divisible processes, matching theorems etc.
  • Gives the complete solution of a number of classical problems
  • Includes supplementary material: sn.pub/extras

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Softcover Book USD 129.99
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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XV
  2. Philosophy and Overview of the Book

    • Michel Talagrand
    Pages 1-12
  3. Matching Theorems, I

    • Michel Talagrand
    Pages 91-127
  4. Bernoulli Processes

    • Michel Talagrand
    Pages 129-171
  5. Trees and the Art of Lower Bounds

    • Michel Talagrand
    Pages 173-197
  6. Processes Related to Gaussian Processes

    • Michel Talagrand
    Pages 233-269
  7. Theory and Practice of Empirical Processes

    • Michel Talagrand
    Pages 271-311
  8. Partition Scheme for Families of Distances

    • Michel Talagrand
    Pages 313-330
  9. Infinitely Divisible Processes

    • Michel Talagrand
    Pages 331-370
  10. The Fundamental Conjectures

    • Michel Talagrand
    Pages 371-398
  11. Applications to Banach Space Theory

    • Michel Talagrand
    Pages 515-593
  12. Back Matter

    Pages 595-626

About this book

The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.

Reviews

“Although he writes a book about inequalities of stochastic processes, Talagrand focuses on modern abstract methods, completely abdicating the ‘classical approach’. … Talagrand’s goal in this book is, without any doubt, very ambitious. … it contains marvelous ideas that should very likely be in the toolbox of anyone dealing with stochastic processes.” (Antonio Auffinger, Bulletin of the American Mathematical Society, Vol. 53 (1), January, 2016)

“Each chapter begins with an explanation of the overall philosophy and gives a brief survey of the things to come. This makes a rewarding read for everyone with a sound probability background, and for the specialist it is even entertaining and most inspiring. … There are many areas where Talagrand has a very personal view of things which, I am sure, will be food for thought for future generations of probabilists.”(René L. Schilling, The Mathematical Gazette, Vol. 100 (547), 2016)

“The topic of this book is the study of the supremum of certain stochastic processes, more precisely, it describes how to find upper and lower bounds for this suprema. … The book can be interesting for all potential readers who study the modern stochastic methods, for undergraduate and postgraduate students, for specialists in the theory of stochastic processes and for practitioners who treat the trajectories of stochastic models.” (Yuliya S. Mishura, zbMATH, Vol. 1293, 2014)

Authors and Affiliations

  • Institut de Mathématiques, Université Paris VI, Paris Cedex 05, France

    Michel Talagrand

Bibliographic Information

Buy it now

Buying options

Softcover Book USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access