  In this article we prove that the heat kernel attached to the non-archimedean
elliptic pseudodifferential operators determine a Feller semigroup and a
uniformly stochastically continuous C_0 transition function of some strong
Markov processes X with state space (Q_p)^n. We explicitly write the Feller
semigroup and the Markov transition function associated with the heat kernel.
Also, we show that the symbols of these pseudo-differential operators are a
negative definite function and moreover, that this symbols can be represented
as a combination of a positive constant, a continuous homomorphism l : (Q_p)^n
to R and a non-negative, continuous quadratic form q : (Q_p)^n to R.
