Study of dependence for some stochastic processes: symbolic Markov copulae
type: Item
instance of: scholarly article
title: Study of dependence for some stochastic processes: symbolic Markov copulae
zbMATH Open document ID: 1247.60111
author: Tomasz R. Bielecki
author: Jacek Jakubowski
author: Mariusz Niewęgłowski
published in: Stochastic Processes and their Applications
publication date: 2012-03-22T00:00:00Z
review text: 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.
reviewed by: Alexander Schnurr
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 6017609
zbMATH Keywords: Markov process
zbMATH Keywords: Feller process
zbMATH Keywords: Markov consistency
zbMATH Keywords: Markov copulae
zbMATH Keywords: dependence
zbMATH Keywords: pseudo-differential operator
zbMATH Keywords: marginal laws
zbMATH Keywords: symbol
MaRDI profile type: Publication
full work available at URL: j.spa.2011.11.001
OpenAlex ID: W2058106441
cites work: Study of Dependence for Some Stochastic Processes
cites work: Copulas and Markov processes
cites work: Q5342182
cites work: Q3721531
cites work: Characteristic functions and symbols in the theory of Feller processes
cites work: Q5462966
cites work: Q4002114
cites work: Copulas for Markovian dependence
cites work: Q4165953
cites work: Conservativeness of semigroups generated by pseudo differential operators
cites work: Growth and Hölder conditions for the sample paths of Feller processes
cites work: Q3633240
cites work: Q3281461
cites work: Diffusion processes associated with L�vy generators
DOI: 10.1016/J.SPA.2011.11.001
description: scientific article; zbMATH DE number 6017609