Infinite Level GREM-Like K-Processes Existence and Convergence

Autor(es)

Fontes, Luiz Renato ^[1] ; Peixoto, Gabriel R. C. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, IME, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 182, n. 3 MAR 2 2021.
• Citações Web of Science: 0

Resumo

We derive the existence of infinite level GREM-like K-processes by taking the limit of a sequence of finite level versions of such processes as the number of levels diverges. The main step in the derivation is obtaining the convergence of the sequence of underlying finite level clock processes. This is accomplished by perturbing these processes so as to turn them into martingales, and resorting to martingale convergence to obtain convergence for the perturbed clock processes; nontriviality of the limit requires a specific choice of parameters of the original process; we conclude the step by showing that the perturbation washes away in the limit. The perturbation is done by inserting suitable factors into the expression of the clocks, as well as rescaling the resulting expression suitably; the existence of such factors is itself established through martingale convergence. (AU)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático