Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations
Abstract
A Feynman formula is a representation of a solution of an initial (or initialboundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup resolving the problem) by a limit of $n$fold iterated integrals of some elementary functions as $n\to\infty$. In this note we obtain some Feynman formulae for a class of semigroups associated with Feller processes. Finite dimensional integrals in the Feynman formulae give approximations for functional integrals in some FeynmanKac formulae corresponding to the underlying processes. Hence, these Feynman formulae give an effective tool to calculate functional integrals with respect to probability measures generated by these Feller processes and, in particular, to obtain simulations of Feller processes.
 Publication:

arXiv eprints
 Pub Date:
 March 2012
 arXiv:
 arXiv:1203.1199
 Bibcode:
 2012arXiv1203.1199B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Functional Analysis
 EPrint:
 Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 15 N 3 (2012)