LEADER 05849cam a2200673Ii 4500001 99119640493506421 005 20240502081341.0 008 190728t20192019sz b 100 0 eng d 016 7 019637425 |2Uk 019 1139764050 020 9783030295448 |q(paperback) 020 3030295443 |q(paperback) 020 |z9783030295455 |q(electronic book) 029 1 UKMGB |b019637425 029 1 AU@ |b000066489733 035 (NjP)11964049-princetondb 035 |z(OCoLC)1139764050 035 |z(NjP)Voyager11964049 035 |z(NjP)Voyager11964049 035 (OCoLC)on1110438965 040 YDX |beng |erda |cYDX |dBDX |dQGJ |dMUB |dOCLCF |dPAU |dXII |dUKMGB |dOHX |dNTU |dOCL |dPUL 049 PULL 050 4 QA3 |b.L28 no.2253 082 04 519.22 |223 100 1 Gubinelli, Massimiliano, |eauthor. |0http://id.loc.gov/authorities/names/nb2019024097 245 10 Singular random dynamics : |bCetraro, Italy 2016 / |cMassimiliano Gubinelli, Panagiotis E. Souganidis, Nikolay Tzvetkov ; Franco Flandoli, Massimiliano Gubinelli, Martin Hairer, editors. 264 1 Cham, Switzerland : |bSpringer ;[Cetraro] : |bFondazione CIME Roberto Conti, |c[2019] 264 4 |c©2019 300 ix, 313 pages ; |c24 cm. 336 text |btxt |2rdacontent 337 unmediated |bn |2rdamedia 338 volume |bnc |2rdacarrier 490 1 Lecture notes in mathematics, |x0075-8434 ; |v2253 490 1 CIME Foundation series 504 Includes bibliographical references. 505 0 Intro; Preface; General Remarks; The Courses; Final Remarks; Contents; 1 Introduction; References; 2 Lectures on Energy Solutions for the Stationary KPZ Equation; 2.1 Introduction; 2.1.1 Notations and Some Preliminaries; 2.1.2 White Noise; 2.2 The Ornstein-Uhlenbeck Process; 2.3 Gaussian Computations; 2.4 The Itô Trick; 2.5 An Approximation Scheme; 2.5.1 Time Reversal; 2.6 Controlled Processes and Energy Solutions; 2.6.1 Regularization by Noise for Controlled Processes; 2.7 Boltzmann-Gibbs Principle; 2.7.1 A First Computation; 2.8 The Hairer-Quastel Invariance Principle 505 8 2.8.1 The Invariance Principle 2.9 Uniqueness of Energy Solutions; 2.9.1 Mapping to the SHE; 2.9.2 Convergence of the Remainder; References; 3 Pathwise Solutions for Fully Nonlinear First- and Second-Order Partial Differential Equations with Multiplicative Rough Time Dependence; 3.1 Introduction; 3.1.1 Organization of the Notes; 3.2 Motivation and Some Examples; 3.2.1 Motion of Interfaces; 3.2.2 A Stochastic Selection Principle; 3.2.3 Pathwise Stochastic Control Theory; 3.2.4 Mean Field Games; 3.3 The Main Difficulties and the Choice of Stochastic Calculus; 3.3.1 Difficulties 505 8 3.3.2 The Choice of Stochastic Calculus: Stratonovich vs Itô 3.4 Single Versus Multiple Signals, the Method of Characteristics and Nonlinear pde with Linear Rough Dependence on Time; 3.4.1 Single Versus Multiple Signals; 3.4.2 Nonlinear pde with Linear Rough Dependence on Time; 3.4.3 Stochastic Characteristics; 3.5 Fully Nonlinear Equations with Semilinear Stochastic Dependence; 3.6 The Extension Operator for Spatially Homogeneous First-Order Problems; 3.6.1 A Summary of the General Strategy; 3.7 Pathwise Solutions for Equations with Non-smooth Hamiltonians; 3.7.1 Formulae for Solutions 505 8 3.7.2 Pathwise Solutions for Nonsmooth Hamiltonians 3.7.3 Control of Cancellations for Spatially Dependent Hamiltonians; 3.7.4 The Interplay Between the Regularity of the Hamiltonians and the Paths; 3.8 Qualitative Properties; 3.8.1 Domain of Dependence and Finite Speed of Propagation; 3.8.2 Stochastic Intermittent Regularization; 3.8.3 Long Time Behavior of the "Rough" Viscosity Solutions; 3.9 Stochastic Viscosity Solutions; 3.10 Pathwise Solutions to Fully Nonlinear First and Second Order pde with Spatially Dependent Smooth Hamiltonians 505 8 3.10.1 The General Problem, Strategy and Difficulties 3.10.2 Improvement of the Interval of Existence of Smooth Solutions; 3.10.3 The Necessity of the Assumptions; 3.10.4 Convex Hamiltonians and a Single Path; 3.10.5 Multiple Paths; 3.11 Perron's Method; 3.12 Approximation Schemes, Convergence and Error Estimates; 3.12.1 The Scheme Operator; 3.12.2 The Method of Proof; 3.12.3 The Main Examples; 3.12.4 The Need to Regularize the Paths; 3.13 Homogenization; 3.13.1 The Difficulties and General Strategy; 3.13.2 The Single-Noise Case; 3.13.3 The Multiple-Noise Case 505 8 3.14 Stochastically Perturbed Reaction-Diffusion Equations and Front Propagation 540 Current copyright fee: GBP19.00 |c42\0. |5Uk 650 0 Stochastic partial differential equations |vCongresses. 700 1 Gubinelli, Massimiliano, |eauthor, |eeditor. |0http://id.loc.gov/authorities/names/nb2019024097 700 1 Souganidis, Panagiotis E., |eauthor. |0http://id.loc.gov/authorities/names/nb2019024098 700 1 Tzvetkov, Nikolay, |eauthor. |0http://id.loc.gov/authorities/names/nb2019024099 700 1 Flandoli, Franco, |eeditor. |0http://id.loc.gov/authorities/names/no95056351 700 1 Hairer, Martin, |eeditor. |0http://id.loc.gov/authorities/names/nb2008013340 711 2 C.I.M.E. 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