Multifractal analysis of infinite products of stationary jump processes (Q609723)

The authors consider multifractal products of stochastic processes that appear as \[ A(t)=\lim_{n\to\infty} \int_0^t \Lambda^{(i)}(s)ds \] that appear from products of independent rescaled versions \(\Lambda^{(i)}(\cdot)=\Lambda(b^i\cdot)\) of a stationary jump Markov process \(\Lambda\) with i.i.d. exponential interjump times. Particularly, the information dimension and a multifractal spectrum are computed. The multifractal computations are based on partitions naturally created by the Poisson process of jump times. It is shown that the partitions determined by Poisson process are sufficient to determine the spectrum in the setting of this work.