Study of dependence for some stochastic processes: symbolic Markov copulae
The authors study dependence between components of multivariate nice Feller processes, that is, Feller processes with the additional property that the test functions are contained in the domain of the generator. The main question under consideration is: what conditions need to be satisfied by a Markov process with values in \(\mathbb{R}^n\) so that its components are Markovian with respect to the filtration of the entire process and such that they follow prescribed laws? In order to answer this question, the authors introduce a symbolic approach, which relies on the concept of pseudo-differential operator (PDO). They investigate connections between dependence, in the sense described above, and the PDOs. The most important tool in this context is the symbol of the process. This approach leads to relatively simple conditions, which provide solutions to the problem. Examples include the Poisson copula, generalized n-dimensional Markov point processes and Markov jump processes.
scientific article; zbMATH DE number 6017609
scientific article