Perturbed self-intersection local time

S. Alvarez-Andrade

Laboratoire de Mathématiques Appliquées, Université de Technologie de Compieègne, B.P. 529, 60205 Compiègne Cedex, France

Abstract: 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.

Keywords: Self-intersection local time, symmetric random walk, strong approximations.

MSC: Primary 60F15, 60J55; Secondary 60G50

Language: English

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