Admissible formal differentiations for pure discontinuous Markov processes (Q2777845)

The notion of the admissible formal differentiation on a probability space was introduced by \textit{A. Benassi} [C. R. Acad. Sci., Paris, Sér. I 311, No. 7, 457-460 (1990; Zbl 0704.60047)] in order to extend constructions of stochastic differential calculus. A lot of methods of the classical Wiener stochastic calculus are still valid when we have a probability space with admissible differentiation. For example, the Malliavin calculus can be developed [see \textit{Yu. A. Davydov, M. A. Lifshits} and \textit{N. V. Smorodina}, ``Local properties of distributions of stochastic functionals'' (1998; Zbl 0897.60042)]. The author proposes a general approach to construct the admissible differential structure on a space of trajectories of a jump Markov process that does not require any smoothness condition. In his paper [Theory Stoch. Process. 5(21), No. 3-4, 120-126 (1999)] the author proposed such structure for compound Poisson process with arbitrary Lévy measure. In this paper the structure is generalized to the case of general pure discontinuous Markov processes.