Infinite level GREM-like K-processes existence and convergence
| Autor: | Luiz Renato Fontes, Gabriel R. C. Peixoto |
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| Rok vydání: | 2021 |
| Předmět: |
Sequence
Infinite volume Perturbation (astronomy) Statistical and Nonlinear Physics Expression (computer science) 01 natural sciences 010305 fluids & plasmas 0103 physical sciences Convergence (routing) Applied mathematics Limit of a sequence Limit (mathematics) 010306 general physics Martingale (probability theory) PROCESSOS ESTOCÁSTICOS ESPECIAIS Mathematical Physics Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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