Parts formulas involving the Fourier-Feynman transform associated with Gaussian process on Wiener space

2019/03/13 by Chand, Seung Jun, Choi, Jae Gil
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1903.05762

Abstract

In this paper, using a very general Cameron--Storvick theorem on the Wiener space C₀[0,T], we establish various integration by parts formulas involving generalized analytic Feynman integrals, generalized analytic Fourier--Feynman transforms, and the first variation (associated with Gaussian processes) of functionals F on C₀[0,T] having the form F(x)=f(⟨α₁,x⟩, …, ⟨α_n,x⟩) for scale almost every x∈ C₀[0,T], where ⟨α,x⟩ denotes the Paley--Wiener--Zygmund stochastic integral ∫₀^T α(t)dx(t), and \α₁,…,α_n\ is an orthogonal set of nonzero functions in L₂[0,T]. The Gaussian processes used in this paper are not stationary.

Related

• Cameron-Storvick theorem associated with Gaussian paths on function space
• Analytic operator-valued generalized Feynman integral on function space
• Algebraic structure of the L₂ analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space
• Integration-by-Parts Characterizations of Gaussian Processes
• The Gaussian Radon Transform in Classical Wiener Space