Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi; Sang Kil Shim

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 849-868
  • ISSN: 0011-4642

Abstract

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We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , ν ) . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur and Bromley Fresnel class ℱ ( B ) and we finally investigate some Fubini theorems involving CFFT.

How to cite

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Choi, Jae Gil, and Shim, Sang Kil. "Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space." Czechoslovak Mathematical Journal 73.3 (2023): 849-868. <http://eudml.org/doc/299121>.

@article{Choi2023,
abstract = {We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H,B,\nu )$. An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space $B$. Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur and Bromley Fresnel class $\mathcal \{F\}(B)$ and we finally investigate some Fubini theorems involving CFFT.},
author = {Choi, Jae Gil, Shim, Sang Kil},
journal = {Czechoslovak Mathematical Journal},
keywords = {abstract Wiener space; conditional Wiener integral; conditional Fourier-Feynman transform; Fubini theorem},
language = {eng},
number = {3},
pages = {849-868},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space},
url = {http://eudml.org/doc/299121},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Choi, Jae Gil
AU - Shim, Sang Kil
TI - Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 849
EP - 868
AB - We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H,B,\nu )$. An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space $B$. Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur and Bromley Fresnel class $\mathcal {F}(B)$ and we finally investigate some Fubini theorems involving CFFT.
LA - eng
KW - abstract Wiener space; conditional Wiener integral; conditional Fourier-Feynman transform; Fubini theorem
UR - http://eudml.org/doc/299121
ER -

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