Magnetic energies and Feynman-Kac-It\^o formulas for symmetric Markov processes
Probability
2015-08-04 v3 Mathematical Physics
Functional Analysis
math.MP
Abstract
Given a (conservative) symmetric Markov process on a metric space we consider related bilinear forms that generalize the energy form for a particle in an electromagnetic field. We obtain one bilinear form by semigroup approximation and another, closed one, by using a Feynman-Kac-It\^o formula. If the given process is Feller, its energy measures have densities and its jump measure has a kernel, then the two forms agree on a core and the second is a closed extension of the first. In this case we provide the explicit form of the associated Hamiltonian.
Keywords
Cite
@article{arxiv.1409.7743,
title = {Magnetic energies and Feynman-Kac-It\^o formulas for symmetric Markov processes},
author = {Michael Hinz},
journal= {arXiv preprint arXiv:1409.7743},
year = {2015}
}