  Ito's construction of Markovian solutions to stochastic equations driven by a
L\'evy noise is extended to nonlinear distribution dependent integrands aiming
at the effective construction of linear and nonlinear Markov semigroups and the
corresponding processes with a given pseudo-differential generator. It is shown
that a conditionally positive integro-differential operator (of the
L\'evy-Khintchine type) with variable coefficients (diffusion, drift and L\'evy
measure) depending Lipschitz continuously on its parameters (position and/or
its distribution) generates a linear or nonlinear Markov semigroup, where the
measures are metricized by the Wasserstein-Kantorovich metrics. This is a
nontrivial but natural extension to general Markov processes of a long known
fact for ordinary diffusions.
