A course on rough paths : with an introduction to regularity structures / Peter K. Friz, Martin Hairer.

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A course on rough paths : with an introduction to regularity structures / Peter K. Friz, Martin Hairer.

Second edition.

9783030415563 (electronic book)
3030415562 (electronic book)
3030415554
9783030415556

Cham, Switzerland : Springer, [2020]

English

1 online resource.

10.1007/978-3-030-41

QA274.23 .F75 2020

519.2

With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text.

Includes bibliographical references and index.

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Description based on online resource; title from digital title page (viewed on June 15, 2020).

Universitext.

Print version: 9783030415556

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