Geodesic
Brownian local time of the second order
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 75-86 
A. N. Borodin. Brownian local time of the second order. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 75-86. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a4/
@article{ZNSL_2021_505_a4,
     author = {A. N. Borodin},
     title = {Brownian local time of the second order},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {75--86},
     year = {2021},
     volume = {505},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a4/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - Brownian local time of the second order
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 75
EP  - 86
VL  - 505
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a4/
LA  - ru
ID  - ZNSL_2021_505_a4
ER  - 
%0 Journal Article
%A A. N. Borodin
%T Brownian local time of the second order
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 75-86
%V 505
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a4/
%G ru
%F ZNSL_2021_505_a4

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

According to the Ray–Knight description the Brownian local time with respect to the spatial variable is a diffusion process in a certain conditional probability space. This diffusion has a local time. Thus, we come to the definition of local time from the initial Brownian local time. We will call such a process the Brownian local time of the second order. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order.

[1] F. B. Knight, “Random walks and a sojourn density process of Brownian motion”, Trans. Amer. Math. Soc., 109 (1963), 56–86 | DOI | MR | Zbl

[2] D. B. Ray, “Sojourn times of a diffusion process”, Ill. J. Math., 7 (1963), 615–630 | Zbl

[3] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2017

[4] A. N. Borodin, On the distribution of functionals of Brownian local time, LOMI Preprints E-4-85, Leningrad, 1985

[5] A. N. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu. Fakty i formuly, Lan, Sankt-Peterburg, 2016

[6] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1967