A Pseudo-Differential Operator Construction of Markov Processes Using Feynman Path Integrals
Probability
2012-04-26 v1
Abstract
In this paper pseudo-differential operators with negative definite symbols are used to construct time- and space-inhomogeneous Markov processes. This is achieved by using the Markov evolution system associated with the fundamental solution of the corresponding pseudo-differential evolution equation. Negative definite symbols are non-standard and differ significantly from the class of H\"{o}rmander type symbols. The novelty of this work is the derivation and the representation of the fundamental solution as a Feynman path integral. This implies that the transition function of the constructed Markov process can be written as a pseudo-differential operator that has a Feynman path integral as its symbol.
Cite
@article{arxiv.1204.5624,
title = {A Pseudo-Differential Operator Construction of Markov Processes Using Feynman Path Integrals},
author = {Alexander Potrykus},
journal= {arXiv preprint arXiv:1204.5624},
year = {2012}
}