Geodesic
Some effect of drift of the generalized Brownian motion process: existence of the operator-valued generalized Feynman integral
Filomat, Tome 37 (2023) no. 13, p. 4065

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In this paper an analytic operator-valued generalized Feynman integral was studied on a very general Wiener space Ca,b[0,T]. The general Wiener space Ca,b[0,T] is a function space which is induced by the generalized Brownian motion process associated with continuous functions a and b. The structure of the analytic operator-valued generalized Feynman integral is suggested and the existence of the analytic operator-valued generalized Feynman integral is investigated as an operator from L1(R, νδ,a) to L∞(R) where νδ,a is a σ-finite measure on R given by dνδ,a = exp{δVar(a)u2}du, where δ > 0 and Var(a) denotes the total variation of the mean function a of the generalized Brownian motion process. It turns out in this paper that the analytic operator-valued generalized Feynman integrals of functionals defined by the stochastic Fourier-Stieltjes transform of complex measures on the infinite dimensional Hilbert space C′a,b[0,T] are elements of the linear space ⋂ δ>0 L(L1(R, νδ,a),L∞(R)).
DOI : 10.2298/FIL2313065C
Classification : 28C20, 46G12, 46B09.
Keywords: Generalized Brownian motion process, analytic operator-valued generalized function space integral, analytic operator- valued generalized Feynman integral 
Jae Gil Choi. Some effect of drift of the generalized Brownian motion process: existence of the operator-valued generalized Feynman integral. Filomat, Tome 37 (2023) no. 13, p. 4065 . doi: 10.2298/FIL2313065C
@article{10_2298_FIL2313065C,
     author = {Jae Gil Choi},
     title = {Some effect of drift of the generalized {Brownian} motion process: existence of the operator-valued generalized {Feynman} integral},
     journal = {Filomat},
     pages = {4065 },
     year = {2023},
     volume = {37},
     number = {13},
     doi = {10.2298/FIL2313065C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2313065C/}
}
TY  - JOUR
AU  - Jae Gil Choi
TI  - Some effect of drift of the generalized Brownian motion process: existence of the operator-valued generalized Feynman integral
JO  - Filomat
PY  - 2023
SP  - 4065 
VL  - 37
IS  - 13
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2313065C/
DO  - 10.2298/FIL2313065C
LA  - en
ID  - 10_2298_FIL2313065C
ER  - 
%0 Journal Article
%A Jae Gil Choi
%T Some effect of drift of the generalized Brownian motion process: existence of the operator-valued generalized Feynman integral
%J Filomat
%D 2023
%P 4065 
%V 37
%N 13
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2313065C/
%R 10.2298/FIL2313065C
%G en
%F 10_2298_FIL2313065C

Cité par Sources :