Relationships between generalized Wiener integrals and conditional analytic Feynman integrals over continuous paths

Title:

Relationships between generalized Wiener integrals and conditional analytic Feynman integrals over continuous paths

Creator:

Kim, Byoung Soo and Hyun Cho, Dong

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:83c03428-c9f1-4e9f-8b97-e98befd213ec
uuid:83c03428-c9f1-4e9f-8b97-e98befd213ec
issn:0011-4642

Subject:

integrály, integrals, analogue of Wiener space, analytic conditional Feynman integral, change of scale formula, conditional Wiener integral, Wiener integral, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let $C[0,t]$ denote a generalized Wiener space, the space of real-valued continuous functions on the interval $[0,t]$, and define a random vector $Z_n C[0,t]\to\mathbb R^{n+1}$ by Z_n(x)=\biggl(x(0)+a(0), \int_0^{t_1}h(s) {\rm d} x(s)+x(0)+a(t_1), \cdots,\int_0^{t_n}h(s) {\rm d} x(s)+x(0)+a(t_n)\biggr), where $a\in C[0,t]$, $h\in L_2[0,t]$, and $0<t_1 < \cdots< t_n\le t$ is a partition of $[0,t]$. Using simple formulas for generalized conditional Wiener integrals, given $Z_n$ we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions $F$ in a Banach algebra which corresponds to Cameron-Storvick's Banach algebra $\mathcal S$. Finally, we express the generalized analytic conditional Feynman integral of $F$ as a limit of the non-conditional generalized Wiener integral of a polygonal function using a change of scale transformation for which a normal density is the kernel. This result extends the existing change of scale formulas on the classical Wiener space, abstract Wiener space and the analogue of the Wiener space $C[0,t]$., Byoung Soo Kim, Dong Hyun Cho., and Obsahuje bibliografické odkazy

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

609-628

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:3

Harvested from:

CDK

Metadata only:

false