LAGRANGIAN AND HAMILTONIAN FEYNMAN FORMULAE FOR SOME FELLER SEMIGROUPS AND THEIR PERTURBATIONS

@article{Butko2012LAGRANGIANAH,
  title={LAGRANGIAN AND HAMILTONIAN FEYNMAN FORMULAE FOR SOME FELLER SEMIGROUPS AND THEIR PERTURBATIONS},
  author={Yana A. Butko and Ren{\'e} L. Schilling and O. G. Smolyanov},
  journal={Infinite Dimensional Analysis, Quantum Probability and Related Topics},
  year={2012},
  volume={15},
  pages={1250015}
}
A Feynman formula is a representation of a solution of an initial (or initial-boundary) 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 → ∞. 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… 
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23 Citations
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Methods Citations
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23 Citations

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Citation Type

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  • Y. Butko
  • Mathematics
    Fractional Calculus and Applied Analysis
  • 2018
Abstract We consider operator semigroups generated by Feller processes killed upon leaving a given domain. These semigroups correspond to Cauchy–Dirichlet type initial-exterior value problems in this…
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