On Markov processes with decomposable pseudo-differential generators
نویسنده
چکیده
The paper is devoted to the study of Markov processes in finite-dimensional convex cones (especially R and R+) with a decomposable generator, i.e. with a generator of the form L = ∑N n=1Anψn, where An are operators of multiplication on continuous positive functions an(x) (which could be unbounded) and ψn are generators of the Lévy processes (or processes with i.i.d. increments) in R. The following problems are discussed: (i) existence and uniqueness of Markov or Feller process with a given generator, (ii) continuous dependence of the process on the coefficients an and the starting points, (iii) well posedness of the corresponding martingale problem, (iv) generalized solutions to the Dirichlet problem, (v) regularity of boundary points.
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