• 제목/요약/키워드: Kallianpur and Bromley Fresnel class

검색결과 1건 처리시간 0.014초

A CAMERON-STORVICK THEOREM ON C2a,b[0, T ] WITH APPLICATIONS

  • Choi, Jae Gil;Skoug, David
    • 대한수학회논문집
    • /
    • 제36권4호
    • /
    • pp.685-704
    • /
    • 2021
  • The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C2a,b[0, T]. The function space Ca,b[0, T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C2a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C2a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.