Feynman formulae for Feller semigroups

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung


  • Ya A. Butko - , Bauman Moscow State Technical University (Autor:in)
  • O. G. Smolyanov - , Lomonosov Moscow State University (Autor:in)
  • René Leander Schilling - , Professur für Wahrscheinlichkeitstheorie (Autor:in)


The Hamiltonian Feynman formula is proved for a certain class of Feller semigroups. The generators of these semigroups are PDOs whose symbols are continuous functions of a variable and are smooth and negative with respect to a variable for each fixed variable and bounded with respect to a variable for each fixed variable. A strongly continuous contraction semigroup is considered which is positivity preserving. A family of operators is said to be a Chernoff equivalent to the semigroup if this family satisfies the assertions of the Chernoff theorem with respect to this semigroup. A family is Chernoff equivalent to a strongly continuous semigroup generated by the closure of a PDO and the Hamiltonian Feynman formula is valid and is uniformly for values greater than or equal to zero. The family is found to be Chernoff equivalent to the semigroup generated also the Lagrangian Feynman formula holds.


Seiten (von - bis)679-683
FachzeitschriftDoklady Mathematics
PublikationsstatusVeröffentlicht - Okt. 2010


ASJC Scopus Sachgebiete