p-Variation of strong Markov processes

Let xit, t is an element of [0, T], be a strong Markov process with values in a complete separable metric space (X, rho) and with transition probability function P-s,P-t (x, dy), 0 less than or equal to s less than or equal to t less than or equal to T, x is an element of X. For any h is an element of [0, T] and a > 0, consider the function alpha(h,a) = sup{P-s,P-t(x, {y:rho(x,y) greater than or equal to a}):x is an element of X, 0 less than or equal to s less than or equal to t less than or equal to (s +h) boolean AND T}. It is shown that a certain growth condition on alpha(h, a), as a down arrow 0 and h stays fixed, implies the almost sure boundedness of the p-variation of xit, where p depends on the rate of growth.