Continuous flows driving Markov processes and multiplicative $L^p$-semigroups
Abstract
We develop a method of driving a Markov processes through a continuous flow. In particular, at the level of the transition functions we investigate an approach of adding a first order operator to the generator of a Markov process, when the two generators commute. A relevant example is a measure-valued superprocess having a continuous flow as spatial motion and a branching mechanism which does not depend on the spatial variable. We prove that any flow is actually continuous in a convenient topology and we show that a Markovian multiplicative semigroup on an Lp space is generated by a continuous flow, completing the answer to the question whether it is enough to have a measurable structure, like a C0-semigroup of Markovian contractions on an -space with no fixed topology, in order to ensure the existence of a right Markov process associated to the given semigroup. We extend from bounded to unbounded functions the weak generator (in the sense of Dynkin) and the corresponding martingale problem
Cite
@article{arxiv.2411.09407,
title = {Continuous flows driving Markov processes and multiplicative $L^p$-semigroups},
author = {Lucian Beznea and Mounir Bezzarga and Iulian Cimpean},
journal= {arXiv preprint arXiv:2411.09407},
year = {2024}
}