  We develop a stochastic approach to time-dependent DFT with optimally-tuned
range-separated hybrids containing non-local exchange, for calculating optical
spectra. The attractive electron-hole interaction, which leads to the formation
of excitons, is included through a time-dependent linear-response technique
with a non-local exchange interaction which is computed very efficiently
through a stochastic scheme. The method is inexpensive and scales quadratically
with the number of electrons, at almost the same (low) cost of time dependent
Kohn-Sham (TDKS) with local functionals. Our results are in excellent agreement
with experimental data and the efficiency of the approach is demonstrated on
large finite phosphorene sheets containing up to 1958 valence electrons.
