Geodesic
An analogue of the local time of the complex Brownian motion process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 172-184 
A. K. Nikolaev. An analogue of the local time of the complex Brownian motion process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 172-184. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a10/
@article{ZNSL_2021_505_a10,
     author = {A. K. Nikolaev},
     title = {An analogue of the local time of the complex {Brownian} motion process},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {172--184},
     year = {2021},
     volume = {505},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a10/}
}
TY  - JOUR
AU  - A. K. Nikolaev
TI  - An analogue of the local time of the complex Brownian motion process
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 172
EP  - 184
VL  - 505
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a10/
LA  - ru
ID  - ZNSL_2021_505_a10
ER  - 
%0 Journal Article
%A A. K. Nikolaev
%T An analogue of the local time of the complex Brownian motion process
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 172-184
%V 505
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a10/
%G ru
%F ZNSL_2021_505_a10

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

The aim of the present paper is to construct an analogue of local time for the standard Wiener process multiplied by complex constant.

[1] M. S. Agranovich, Sobolevskie prostranstva, ikh obobscheniya i ellipticheskie zadachi v oblastyakh s gladkoi i lipshitsevoi granitsei, MTsNMO, M., 2013, 378 pp.

[2] A. N. Borodin, I. A. Ibragimov, “Predelnye teoremy dlya funktsionalov ot sluchainykh bluzhdanii”, Tr. MIAN SSSR, 195, 1994, 3–285

[3] S. M. Berman, “Local times and sample function properties of stationary Gaussian process”, Trans. Amer. Math. Soc., 137 (1969), 277–299 | DOI | MR | Zbl

[4] Kai Lai Chung, Zhongxin Zhao, From Brownian motion to Schrodinger's equation, Springer-Verlag, Berlin–Heidelberg, 1995

[5] I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Local time and local reflection of the Wiener process”, Operator Theory and Harmonic Analysis, OTHA 2020, Springer Proceedings in Mathematics Statistics, 358, eds. Karapetyants A.N., Pavlov I.V., Shiryaev A.N., Springer, Cham, 2020

[6] D. K. Faddeev, B. Z. Vulikh, N. N. Uraltseva, Izbrannye glavy analiza i vysshei algebry, Izd-vo Leningr. un-ta, L., 1981, 200 pp.