Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-04T06:47:47.638Z Has data issue: false hasContentIssue false

Preface

Published online by Cambridge University Press:  05 June 2012

Peter K. Friz
Affiliation:
University of Cambridge
Get access

Summary

This book is split into four parts. Part I is concerned with basic material about certain ordinary differential equations, paths of Hölder and variation regularity, and the rudiments of Riemann–Stieltjes and Young integration. Nothing here will be new to specialists, but the material seems rather spread out in the literature and we hope it will prove useful to have it collected in one place.

Part II is about the deterministic core of rough path theory, à la T. J. Lyons, but actually inspired by the direct approach of A. M. Davie. Although the theory can be formulated in a Banach setting, we have chosen to remain in a finitedimensional setting; our motivation for this decision comes from the fact that the bulk of classic texts on Brownian motion and stochastic analysis take place in a similar setting, and these are the grounds on which we sought applications.

In essence, with rough paths one attempts to take out probability from the theory of stochastic differential equations – to the extent possible. Probability still matters, but the problems are shifted from the analysis of the actual SDEs to the analysis of elementary stochastic integrals, known as Lévy's stochastic area. In Part III we start with a detailed discussion of how multidimensional Brownian motion can be turned into a (random) rough path; followed by a similar study for (continuous) semi-martingales and large classes of multidimensional Gaussian – and Markovian – processes.

Type
Chapter
Information
Multidimensional Stochastic Processes as Rough Paths
Theory and Applications
, pp. xii - xiii
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Preface
  • Peter K. Friz, University of Cambridge, Nicolas B. Victoir
  • Book: Multidimensional Stochastic Processes as Rough Paths
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511845079.001
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Preface
  • Peter K. Friz, University of Cambridge, Nicolas B. Victoir
  • Book: Multidimensional Stochastic Processes as Rough Paths
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511845079.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preface
  • Peter K. Friz, University of Cambridge, Nicolas B. Victoir
  • Book: Multidimensional Stochastic Processes as Rough Paths
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511845079.001
Available formats
×