  We demonstrate numerically that a pure time-harmonic bias AC current of some
particular amplitude $\tau_f$ and angular frequency $\omega_f$ can excite the
chaotic magnetization dynamics in a Josephson-like antiferromagnetic (AFM) spin
Hall oscillator (SHO) having a biaxial magnetic anisotropy of an AFM layer. The
nature of such a stochastic generation regime in a Josephson-like AFM SHO could
be explained by the random hopping of the SHO's work point between several
quasi-stable states under the action of applied AC current. We revealed that
depending on the $\omega_f/\tau_f$ ratio several stochastic generation regimes
interspersed with regular generation regimes can be achieved in an AFM SHO that
can be used in spintronic sources of random signals and various nano-scale
devices utilizing random signals including the spintronic p-bit device
considered in this paper. The obtained results are important for the
development and optimization of spintronic devices able to generate and process
(sub-)THz-frequency random signals promising for ultra-fast probabilistic
computing, cryptography, secure communications, etc.
