Magnetic energies and Feynman-Kac-It\^o formulas for symmetric Markov processes

Michael Hinz

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arXiv · 1409.7743

Magnetic energies and Feynman-Kac-It\^o formulas for symmetric Markov processes

Michael Hinz

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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.

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BibTeX RIS

Michael Hinz. 2014-09-26. Magnetic energies and Feynman-Kac-It\^o formulas for symmetric Markov processes. https://arxiv.org/abs/1409.7743

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