  The authors present a method of indicator random processes, applicable to
constructing models of jump processes associated with diffusion process.
Indicator random processes are processes that take only two values: 1 and 0, in
accordance with some probabilistic laws. It is shown that the indicator random
process is invariant when reduced to an arbitrary positive degree. Equations
with random coefficients used in modeling dynamic systems, when applying the
method of indicator random processes, can take into account the possibility of
adaptation to external changes, including random ones, in order to preserve
indicators important for the existence of the system, which can be continuous
or discrete. In the case of indicator random processes, defined as functions of
the Poisson process, equations for dynamic processes in a media with abruptly
changing properties are constructed and studied. To study the capabilities of
the proposed method, dynamic models of the diffusion process in media with
delay centers and diffusion processes during transitions by switching from one
subspace to another were studied. For these models, equations for
characteristic functions are constructed. Using the method of indicator random
processes, a characteristic function for the Kac model was constructed. It is
shown that in the case of dependence of the indicator random process on the
Poisson process, the equation for the characteristic function corresponds to
the telegraph equation. This result coincides with the result of Kac.
