On Range and Local Time of Many-dimensional Submartingales

Autor(es)

Menshikov, Mikhail ^[1] ; Popov, Serguei ^[2]

Afiliação do(s) autor(es)

^[1] Univ Durham, Dept Math Sci, Durham DH1 3LE - England

^[2] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Dept Stat, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF THEORETICAL PROBABILITY; v. 27, n. 2, p. 601-617, JUN 2014.
• Citações Web of Science: 3

Resumo

We consider a discrete-time process adapted to some filtration which lives on a (typically countable) subset of a{''}e (d) , da parts per thousand yen2. For this process, we assume that it has uniformly bounded jumps, and is uniformly elliptic (can advance by at least some fixed amount with respect to any direction, with uniformly positive probability). Also, we assume that the projection of this process on some fixed vector is a submartingale, and that a stronger additional condition on the direction of the drift holds (this condition does not exclude that the drift could be equal to 0 or be arbitrarily small). The main result is that with very high probability the number of visits to any fixed site by time n is less than for some delta > 0. This in its turn implies that the number of different sites visited by the process by time n should be at least n(1/2+delta). (AU)

• Processo FAPESP: 09/52379-8 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/07000-0 - Passeios aleatórios e tópicos relacionados
• Beneficiário: Serguei Popov
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional