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1. |
Record Nr. |
UNINA9910151937003321 |
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Autore |
del Barrio Eustasio |
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Titolo |
Lectures on Empirical Processes [[electronic resource] ] : Theory and Statistical Applications / / Eustasio del Barrio, Paul Deheuvels, Sara van de Geer |
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Pubbl/distr/stampa |
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Zuerich, Switzerland, : European Mathematical Society Publishing House, 2007 |
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ISBN |
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Descrizione fisica |
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1 online resource (263 pages) |
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Collana |
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EMS Series of Lectures in Mathematics (ELM) ; , 2523-5176 |
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Classificazione |
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Soggetti |
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Probability & statistics |
Stochastics |
Probability theory and stochastic processes |
Statistics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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The theory of empirical processes constitutes the mathematical toolbox of asymptotic statistics. Its growth was accelerated by the 1950s work on the Functional Central Limit Theorem and the Invariance Principle. The theory has developed in parallel with statistical methodologies, and has been successfully applied to a large diversity of problems related to the asymptotic behaviour of statistical procedures. The three sets of lecture notes in the book offer a wide panorama of contemporary empirical processes theory. Techniques are developed in the framework of probability in Banach spaces, Hungarian-style strong approximations, using tools from general stochastic process theory. Other tools appear in this text in connection with historical as well as modern applications, such as goodness-of-fit tests, density estimation or general M-estimators. This book gives an excellent overview of the broad scope of the theory of empirical processes. It will be an invaluable aid for students and researchers interested in an advanced and well-documented approach to the selected topics. |
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2. |
Record Nr. |
UNINA9910814026203321 |
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Autore |
Strade Helmut |
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Titolo |
Simple lie algebras over fields of positive characteristic . Volume I Structure theory / / Helmut Strade |
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Pubbl/distr/stampa |
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Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2017 |
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©2017 |
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ISBN |
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3-11-051523-7 |
3-11-051544-X |
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Edizione |
[Second edition.] |
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Descrizione fisica |
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1 online resource (542 pages) |
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Collana |
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De Gruyter Expositions in Mathematics, , 0938-0572 ; ; Volume 38 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Frontmatter -- Contents -- Introduction -- Chapter 1. Toral subalgebras in p-envelopes -- Chapter 2. Lie algebras of special derivations -- Chapter 3. Derivation simple algebras and modules -- Chapter 4. Simple Lie algebras -- Chapter 5. Recognition theorems -- Chapter 6. The isomorphism problem -- Chapter 7. Structure of simple Lie algebras -- Chapter 8. Pairings of induced modules -- Chapter 9. Toral rank 1 Lie algebras -- Notation -- Bibliography -- Index |
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The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p › 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p › 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p › 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p › 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification |
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Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopesLie algebras of special derivationsDerivation simple algebras and modulesSimple Lie algebrasRecognition theoremsThe isomorphism problemStructure of simple Lie algebrasPairings of induced modulesToral rank 1 Lie algebras |
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