000			nam a22 4500
999			_c32531 _d32531
008			230901b xxu||||| |||| 00| 0 eng d
020			_a9783030890025
082			_a519.2 _bPAR
100			_aPardoux, Etienne
245			_aStochastic partial differential equations : an introduction
260			_bSpringer, _c2021 _aCham :
300			_aviii, 74 p. ; _c24 cm
365			_d59.99 _bEUR _c94.90
490			_aSpringer briefs in Mathematics
504			_aIncludes bibliographical references and index.
520			_aThis book gives a concise introduction to the classical theory of stochastic partial differential equations (SPDEs). It begins by describing the classes of equations which are studied later in the book, together with a list of motivating examples of SPDEs which are used in physics, population dynamics, neurophysiology, finance and signal processing. The central part of the book studies SPDEs as infinite-dimensional SDEs, based on the variational approach to PDEs. This extends both the classical Ito formulation and the martingale problem approach due to Stroock and Varadhan. The final chapter considers the solution of a space-time white noise-driven SPDE as a real-valued function of time and (one-dimensional) space. The results of J. Walsh's St Flour notes on the existence, uniqueness and Holder regularity of the solution are presented. In addition, conditions are given under which the solution remains nonnegative, and the Malliavin calculus is applied. Lastly, reflected SPDEs and their connection with super Brownian motion are considered. At a time when new sophisticated branches of the subject are being developed, this book will be a welcome reference on classical SPDEs for newcomers to the theory.
650			_aDominated convergence theorem
650			_aFubini's theorem
650			_a Local martingale
650			_aOrthonormal basis
650			_aProbability
942			_2ddc _cBK