Cameron-Storvick theorem associated with Gaussian paths on function space

2021/04/13 by Choi, Jae Gil
#28C20 #46B09 #46G12 #60G15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2104.06542

Abstract

The purpose of this paper is to provide a more general Cameron-Storvick theorem for the generalized analytic Feynman integral associated with Gaussian process \mathcal Z_k on a very general Wiener space C_a,b[0,T]. The general Wiener space C_a,b[0,T] can be considered as the set of all continuous sample paths of the generalized Brownian motion process determined by continuous functions a(t) and b(t) on [0,T]. As an interesting application, we apply this theorem to evaluate the generalized analytic Feynman integral of certain monomials in terms of Paley-Wiener-Zygmund stochastic integrals.

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