000			02016 a2200229 4500
005			20181030124106.0
008			181030b xxu||||| |||| 00| 0 eng d
020			_a9783319083315
040			_cIIT Kanpur
041			_aeng
082			_a519.2 _bF919c
100			_aFriz, Peter K.
245			_aA course on rough paths _bwith an introduction to regularity structures _cPeter K. Friz and Martin Hairer
260			_bSpringer _c2014 _aSwitzerland
300			_axiv, 251p
440			_aUniversitext / edited by Sheldon Axler
520			_aLyons’ rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis. When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension – the theory of regularity structures – and the last parts of this book are devoted to a gentle introduction. Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.
650			_aMathematical statistics
650			_aPartial differential equations
700			_aHairer, Martin
942			_cBK
999			_c559534 _d559534