Abstract
Feller processes are a particular kind of continuous-time Markov processes, which generalize the class of stochastic processes with stationary and independent increments or Levy processes. A stochastic process (ξt)t≥0 in R is called Feller process if it generates a strongly continuous positivity preserving contraction semigroup (Tt)t≥0 on the space C∞(R) of continuous functions vanishing at infinity (i.e. Feller semigroup): Ttf(q) = E[f(ξt)] for any f ∈ C∞(R). Note that diffusion processes in R also belong to the class of Feller processes. It is well known that (under a mild richness condition on the domain) the infinitesimal generator A of a Feller semigroup is a pseudo-differential operator (ΨDO, for short), i.e. an operator of the form
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