Limit Theorems for Multi-Indexed Sums of Random Variables

Oleg Klesov

ISBN 10: 3662443872 / ISBN 13: 9783662443873

Editore: Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE, 2014

Riguardo questo articolo

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes.Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals.The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.

Codice articolo LU-9783662443873

Dati bibliografici

• Titolo: Limit Theorems for Multi-Indexed Sums of Random Variables
• Editore: Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 3662443872
• ISBN 13: 9783662443873
• Rilegatura: Hardback
• Edizione: 2014 ed.
• Condizione: New
• Dimensioni: 15,88 L x 3,18 A x 23,5 P centimetri 15,88 centimetri di larghezza per 3,18 centimetri di altezza per 23,5 centimetri di profondità
• Peso: 816 grammi

Descrizione articolo

Riassunto

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes.

Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals.

The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.

Informazioni sull'autore

Oleg Klesov graduated from Kiev Shevchenko University in 1977 and obtained his PhD in 1979, followed by his habilitation in 2001. He is currently Professor at the National Technical University of Ukraine “Kyiv Polytechnic Institute”. During his academic career, he has held several positions as Invited Professor at Lublin (Poland), Debrecen (Hungary), Marburg, Koeln, Paderborn (Germany), Gainesville (USA), Cergy Pontoise (France), and Lakehead (Canada). His main scientific interests are in probability theory, stochastic processes and real analysis.