  For each prime $p$, a diffusion constant together with a positive exponent
specify a Vladimirov operator and an associated $p$-adic diffusion equation.
The fundamental solution of this pseudo-differential equation gives rise to a
measure on the Skorokhod space of $p$-adic valued paths that is concentrated on
the paths originating at the origin. We calculate the first exit probabilities
of paths from balls and estimate these probabilities for the brownian bridges.
