  This paper studies acceleration processes of background thermal electrons in
X-ray binary jets via turbulent stochastic interactions and shock collisions.
By considering turbulent magnetized jets mixed with fluctuation magnetic fields
and ordered, large-scale one, and numerically solving the transport equation
along the jet axis, we explore the influence of such as magnetic turbulence,
electron injections, location of an acceleration region, and various cooling
rates on acceleration efficiency. The results show that (1) the existence of
the dominant turbulent magnetic fields in the jets is necessary to accelerate
background thermal electrons to relativistic energies. (2) Acceleration rates
of electrons depend on magnetohydrodynamic turbulence types, from which the
turbulence type with a hard slope can accelerate electrons more effectively.
(3) An effective acceleration region should be located at the distance
$>10^3R_{\rm g}$ away from the central black hole ($R_{\rm g}$ being a
gravitational radius). As a result of acceleration rates competing with various
cooling rates, background thermal electrons obtain not only an increase in
their energies but also their spectra are broadened beyond the given initial
distribution to form a thermal-like distribution. (4) The acceleration
mechanisms explored in this work can reasonably provide the electron maximum
energy required for interpreting high-energy $\gamma$-ray observations from
microquasars, but it needs to adopt some extreme parameters in order to predict
a possible very high-energy $\gamma$-ray signal.
