Geodesic
On a family of complex-valued stochastic processes
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 38-41.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce a family $r_\lambda$, $\lambda\in\mathbb C$ of complex-valued stochastic processes making it possible to construct a probabilistic representation for the resolvent of the operator $-\frac12\frac{d^2}{dx^2}$. For $\lambda=0$ the process $r_\lambda$ is real-valued and coincides with the Brownian local time process.
Keywords: random processes, local time. 
@article{DANMA_2021_501_a6,
     author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
     title = {On a family of complex-valued stochastic processes},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {38--41},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a6/}
}
TY  - JOUR
AU  - I. A. Ibragimov
AU  - N. V. Smorodina
AU  - M. M. Faddeev
TI  - On a family of complex-valued stochastic processes
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 38
EP  - 41
VL  - 501
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_501_a6/
LA  - ru
ID  - DANMA_2021_501_a6
ER  - 
%0 Journal Article
%A I. A. Ibragimov
%A N. V. Smorodina
%A M. M. Faddeev
%T On a family of complex-valued stochastic processes
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 38-41
%V 501
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_501_a6/
%G ru
%F DANMA_2021_501_a6
I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. On a family of complex-valued stochastic processes. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 38-41. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a6/

[1] Ladyzhenskaya O.A., Uraltseva N.N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

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

[3] Birman M.Sh., Solomyak M.Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Lan, Sankt-Peterburg–Moskva–Krasnodar, 2010

[4] Borodin A.N., Ibragimov I.A., “Predelnye teoremy dlya funktsionalov ot sluchainykh bluzhdanii”, Tr. MIAN SSSR, 195, 1994, 3–286

[5] Berman S., “Gaussian processes with stationary increments: local times and sample function properties”, Ann. Math. Stat., 41:4 (1970), 1260–1272 | DOI | MR | Zbl

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