Topological complexity of smooth random functions [Documento electrónico] : école d'été de probabilités de Saint-Flour XXXIX-2009 / Robert J. Adler, Jonathan E. Taylor
Language: eng.Country: Germany.Publication: Berlin, Heidelberg : Springer, 2011Description: VIII, 122 p. : il.ISBN: 978-3-642-19580-8.Series: Lecture Notes in MathematicsSubject - Topical Name: Processos gaussianos | Campos aleatórios Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA274.25.SPR FCT 81896 Strong and weak approximation of semilinear stochastic evolution equations | QA274.25.SPR FCT 82189 A minicourse on stochastic partial differential equations | QA274.25.SPR FCT 82463 Stochastic differential equations in infinite dimensions, with applications to stochastic partial differential equations | QA274.4.SPR FCT 82499 Topological complexity of smooth random functions, école d'été de probabilités de Saint-Flour XXXIX-2009 | QA274.4.SPR FCT 82879 Wiener chaos, moments, cumulants and diagrams, a survey with computer implementation | QA274.45.SPR FCT 82599 Invariant random fields on spaces with a group action | QA274.7.SPR FCT Basics of probability and stochastic processes |
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These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
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