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Valentin Vladimirovich Petrov | University St. Petersburg - Rússia

Processo: 01/13969-2
Linha de fomento:Auxílio à Pesquisa - Pesquisador Visitante - Internacional
Vigência: 29 de abril de 2002 - 29 de maio de 2002
Área do conhecimento:Ciências Exatas e da Terra - Probabilidade e Estatística
Pesquisador responsável:Pablo Augusto Ferrari
Beneficiário:Pablo Augusto Ferrari
Pesquisador visitante: Valentin Vladimirovich Petrov
Inst. do pesquisador visitante: Saint-Petersburg State University (SPbSU), Rússia
Instituição-sede: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brasil
Vinculado ao auxílio:99/11962-9 - Fenômenos críticos em processos evolutivos e sistemas em equilíbrio, AP.TEM
Assunto(s):Teoremas limites  Intercâmbio de pesquisadores  Cooperação internacional 

Resumo

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)