  We present an existence result for L\'evy-type processes which requires only
weak regularity assumptions on the symbol $q(x,\xi)$ with respect to the space
variable $x$. Applications range from existence and uniqueness results for
L\'evy-driven SDEs with H\"older continuous coefficients to existence results
for stable-like processes and L\'evy-type processes with symbols of variable
order. Moreover, we obtain heat kernel estimates for a class of L\'evy and
L\'evy-type processes. The paper includes an extensive list of L\'evy(-type)
processes satisfying the assumptions of our results.
