Limit Theorems for Multi-Indexed Sums of Random Variables

• Κύριος συγγραφέας: Klesov, Oleg (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
• Σειρά: Probability Theory and Stochastic Modelling, 71
• Θέματα: Mathematics.; Probabilities.; Physics.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Mathematical Methods in Physics.

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 establish...

Πίνακας περιεχομένων:

• 1.Notation and auxiliary results
• 2.Maximal inequalities for multiple sums
• 3.Weak convergence of multiple sums
• 4.Weak law of large numbers for multiple sums
• 5.Almost sure convergence for multiple series
• 6.Boundedness of multiple series
• 7.Rate of convergence of multiple sums
• 8.Strong law of large numbers for independent non-identically distributed random variables
• 9.Strong law of large numbers for independent identically distributed random variables
• 10.Law of the iterated logarithm
• 11.Renewal theorem for random walks with multidimensional time
• 12.Existence of moments of the supremum of multiple sums and the strong law of large numbers
• 13.Complete convergence.