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Perturbed self-intersection local time
S. Alvarez-Andrade Laboratoire de Mathématiques Appliquées, Université de Technologie de Compieègne, B.P. 529, 60205 Compiègne Cedex, France
Аннотация:
We consider a symmetric random walk related to independent Rademacher random variables. Our aim is to study some modified versions of the so called self-intersection local time of this random walk. The modified versions of the self-intersection local time are obtained by introducing a time $t$ and a sequence of independent with the same distribution uniform on $(0,1)$ random variables $Y_i$'s, independent of the random walk. In this work, we study a distance between the standard self-intersection local time of the random walk and some modified versions (perturbed) of it. We also state a two-parameter strong approximation for the centered local time of the hybrids of empirical and partial sums processes by a process defined by a Wiener sheet combined with an independent Brownian motion.
Ключевые слова:
Self-intersection local time, symmetric random walk, strong approximations.
Образец цитирования:
S. Alvarez-Andrade, “Perturbed self-intersection local time”, Theory Stoch. Process., 18(34):1 (2012), 45–57
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp17 https://www.mathnet.ru/rus/thsp/v18/i1/p45
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Страница аннотации: | 82 | PDF полного текста: | 34 | Список литературы: | 30 |
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