  We study the stochastic variation of blazar emission under a 2-D spatially
resolved leptonic jet model we previously developed. Random events of particle
acceleration and injection in small zones within the emission region are
assumed to be responsible for flux variations. In addition to producing
spectral energy distributions that describe the observed flux of Mrk 421, we
further analyze the timing properties of the simulated light curves, such as
the power spectral density (PSD) at different bands, flux-flux correlations, as
well as the cross-correlation function between X-rays and TeV {\gamma}-rays. We
find spectral breaks in the PSD at a timescale comparable to the dominant
characteristic time scale in the system, which is usually the pre-defined decay
time scale of an acceleration event. Cooling imposes a delay, and so PSDs taken
at lower energy bands in each emission component (synchrotron or inverse
Compton) generally break at longer timescales. The flux-flux correlation
between X-rays and TeV {\gamma}-rays can be either quadratic or linear,
depending on whether or not there are large variation of the injection into the
particle acceleration process. When the relationship is quadratic, the TeV
flares lag the X-ray flares, and the optical & GeV flares are large enough to
be comparable to the ones in X-ray. When the relationship is linear, the lags
are insignificant, and the optical & GeV flares are small.
