Valentin Vladimirovich Petrov | University St. Petersburg - Rússia

• Grant number: 01/13969-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: April 29, 2002
• End date: May 29, 2002
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics
• Principal Investigator: Pablo Augusto Ferrari
• Grantee: Pablo Augusto Ferrari
• Visiting researcher: Valentin Vladimirovich Petrov
• Visiting researcher institution: Saint-Petersburg State University (SPbSU), Russia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 99/11962-9 - Critical Phenomena in envolving processes and equilibrium systems, AP.TEM

Abstract

I plan to continue my investigations related to limit theorems of probability theory and summarized in my monograph “Limit Theorems of Probability Theory”, Oxford University Press, 1995. Special attention will be paid to strong limit theorems for sequences of independent random variables including strong laws of large numbers and laws of the iterated logarithm type. In particular, I will study broad conditions of the applicability of the classical law of the iterated logarithm and its generalizations (without any moment conditions) to sequences of independent (as well as dependent) random variables. Estimates of the growth of sums of random variables with probability 1 will be investigate. Some generalizations of the Borel–Cantelli lemma will be obtained; this lemma plays a fundamental role in proving strong limit theorems of all kinds, I hope to contribute with Brazilian researchers on these topics and on other topics proposed by them. (AU)