Variable order subordination in the sense of Bochner and pseudo-differential operators

For a large class of pseudo-differential operators with a negative definite symbol q(x, xi) in the sense of Hoh and for a large family of x-dependent Bernstein functions f(x, .) we prove that the pseudo-differential operator with symbol -f(x, q(x, xi)) has an extension generating a Feller semigroup. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim