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We present the results of our power spectral analysis for the BL Lac objectPKS 0735+178 utilizing the Fermi-LAT survey at high-energy $\gamma$-rays,several ground-based optical telescopes, and single-dish radio telescopesoperating at GHz frequencies. The novelty of our approach is that, by combininglong-term and densely sampled intra-night light curves in the optical regime,we were able to construct for the first time the optical power spectrum of theblazar for a time domain extending from 23 years down to minutes. Our analysisreveals that: (i) the optical variability is consistent with a pure red noise,for which the power spectral density can well be approximated by a singlepower-law throughout the entire time domain probed; (ii) the slope of powerspectral density at high-energy $\gamma$-rays ($\sim 1$), is significantlyflatter than that found at radio and optical frequencies ($\sim 2$) within thecorresponding time variability range; (iii) for the derived power spectra wedid not detect any low-frequency flattening, nor do we see any evidence forcut-offs at the highest frequencies down to the noise floor levels due tomeasurement uncertainties. We interpret our findings in terms of a model wherethe blazar variability is generated by the underlying single stochastic process(at radio and optical frequencies), or a linear superposition of such processes(in the $\gamma$-ray regime). Along with the detailed PSD analysis, we alsopresent the results of our extended (1998-2015) intra-night optical monitoringprogram and newly acquired optical photo-polarimetric data for the source.

Multi-wavelength variability study of the classical BL Lac object PKS 0735+178 on timescales ranging from decades to minutes