In first section of paper we will prove that for linear Markov dynamical systems an equilibrium asymptotic stochastic stability is equivalent to exponential p-stability for sufficiently small positive values p. Then we will prove that exponential p-stability of linearized in vicinity of equilibrium Markov dynamical system guarantees equilibrium asymptotic (local) stochastic stability.This result permits to construct such Lyapunov quadratic functional, which one may use for local equilibrium stochastic stability of sufficiently smooth nonlinear Markov dynamical systems.