| Title:
|
Relationships between generalized Wiener integrals and conditional analytic Feynman integrals over continuous paths (English) |
| Author:
|
Kim, Byoung Soo |
| Author:
|
Cho, Dong Hyun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
609-628 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $Z_n\colon C[0,t]\to \mathbb R^{n+1}$ 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 $C[0,t]$. (English) |
| Keyword:
|
analogue of Wiener space |
| Keyword:
|
analytic conditional Feynman integral |
| Keyword:
|
change of scale formula |
| Keyword:
|
conditional Wiener integral |
| Keyword:
|
Wiener integral |
| MSC:
|
28C20 |
| MSC:
|
60G05 |
| MSC:
|
60G15 |
| MSC:
|
60H05 |
| idZBL:
|
Zbl 06770120 |
| idMR:
|
MR3697906 |
| DOI:
|
10.21136/CMJ.2017.0248-15 |
| . |
| Date available:
|
2017-09-01T12:19:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146849 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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