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دانلود کتاب A Course on Rough Paths: With an Introduction to Regularity Structures
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A Course on Rough Paths: With an Introduction to Regularity Structures
ویرایش: [2 ed.] نویسندگان: Peter K. Friz, Martin Hairer سری: ISBN (شابک) : 3030415554, 9783030415556 ناشر: Springer سال نشر: 2020 تعداد صفحات: [354] زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 4 Mb
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توضیحاتی درمورد کتاب به خارجی
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.
From the reviews of the first edition:
"Can easily be used as a support for a graduate course ...
Presents in an accessible way the unique point of view of two
experts who themselves have largely contributed to the theory"
- Fabrice Baudouin in the Mathematical Reviews
"It is easy to base a graduate course on rough paths on this …
A researcher who carefully works her way through all of the
exercises will have a very good impression of the current state
of the art" - Nicolas Perkowski inZentralblatt MATH
04
02
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.
13
02
Peter K. Friz is presently Einstein Professor of Mathematics at
TU and WIAS Berlin. His previous professional affiliations
include Cambridge University and Merrill Lynch, and he holds a
PhD from the Courant Institute of New York University. He has
made contributions to the understanding of the Navier-Stokes
equation as dynamical system, pioneered new asymptotic
techniques in financial mathematics and has written many
influential papers on the applications of rough path theory to
stochastic analysis, ranging from the interplay of rough paths
with Malliavin calculus to a (rough-) pathwise view on
non-linear SPDEs. Jointly with N. Victoir he authored a
monograph on stochastic processes as rough paths.
Martin Hairer KBE FRS is currently Professor of Mathematics at
Imperial College London. He has mostly worked in the fields of
stochastic partial differential equations in particular, and in
stochastic analysis and stochastic dynamics in general. He made
fundamental advances in various directions such as the study of
hypoelliptic and/or hypocoercive diffusions, the development of
an ergodic theory for stochastic PDEs, the systematisation of
the construction of Lyapunov functions for stochastic systems,
the development of a general theory of ergodicity for
non-Markovian systems, multiscale analysis techniques, etc.
Most recently, he has worked on applying rough path techniques
to the analysis of certain ill-posed stochastic PDEs and
introduced the theory of regularity structures. For this work
he was awarded the Fields Medal at the 2014 ICM in Seoul.
18
02
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.
From the reviews of the first edition:
"Can easily be used as a support for a graduate course ...
Presents in an accessible way the unique point of view of two
experts who themselves have largely contributed to the theory"
- Fabrice Baudouin in theMathematical Reviews
"It is easy to base a graduate course on rough paths on this …
A researcher who carefully works her way through all of the
exercises will have a very good impression of the current state
of the art" - Nicolas Perkowski inZentralblatt
MATH
19
02
Provides a self-contained introduction to rough path analysis
with many exercises
Includes applications to stochastic partial differential
equations
Covers the basics of the new theory of regularity
structures
06
05
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