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Valentin Vladimirovich Petrov | University St. Petersburg - Rússia

Grant number: 01/13969-2
Support type:Research Grants - Visiting Researcher Grant - International
Duration: April 29, 2002 - 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
Home 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)