A Course on Rough Paths : With an Introduction to Regularity Structures. 2nd ed. 2020

種類:

電子ブック

責任表示:

by Peter K. Friz, Martin Hairer

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Friz, Peter K.
• Hairer, Martin.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783030415563 [3030415562]    

注記:

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.
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 re

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