Erdös-Rényi law for the local time of the hybrid process

S. Alvarez-Andrade
Theory of Stochastic Processes
Vol.19 (35), no.2, 2014, pp.1-9
Our aim in this paper is to study the Erdös-Rényi law for the local time of the hybrid of empirical and partial sums process. The corresponding local time can be see as a modified version of the local time of the symmetric random walk by introducing a time t and a sequence of independent with the same distribution random variables X_i's, independent of the random walk.