  In this article, we study a large class of radial probability density
functions defined on the p-adic numbers from which it is possible to obtain
certain non-archimedean pseudo-differential operators. These operators are
associated with certain p-adic master equations of some models of complex
systems (such as glasses, macromolecules, and proteins). We prove via the
theory of distributions some properties corresponding to the heat Kernel
associated with these pseudo-differential operators. Also, study some
properties corresponding to the fundamental solution of these p-adic equations.
Finally, we will study strong Markov processes, the first passage time problem
and the survival probability (of the trajectories of these processes)
corresponding to radial probability density functions connected with energy
landscapes of the linear and logarithmic types.
