Geodesic
Distributions of functionals of diffusions with non-standard switching
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 87-101
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper dials with the results that allow us to calculate the joint distributions of functionals of diffusions with switchings that occur in random time moments depending on the diffusion trajectory. Standard switching from one set of diffusion coefficients to another set occur in random moments of time corresponding to the moments of jumps of the Poisson process, independent of the initial diffusions. More general non-standard switching occur when the integral functional of the trajectory reaches the value equal to the exponentially distributed variable. With a unit integrand such switching become standard. 
@article{ZNSL_2020_495_a4,
     author = {A. N. Borodin},
     title = {Distributions of functionals of diffusions with non-standard switching},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {87--101},
     year = {2020},
     volume = {495},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a4/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - Distributions of functionals of diffusions with non-standard switching
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 87
EP  - 101
VL  - 495
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a4/
LA  - ru
ID  - ZNSL_2020_495_a4
ER  - 
%0 Journal Article
%A A. N. Borodin
%T Distributions of functionals of diffusions with non-standard switching
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 87-101
%V 495
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a4/
%G ru
%F ZNSL_2020_495_a4
A. N. Borodin. Distributions of functionals of diffusions with non-standard switching. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 87-101. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a4/

[1] A. N. Borodin, “Raspredeleniya funktsionalov ot diffuzii s pereklyucheniyami”, Zap. nauchn. semin. POMI, 454, 2016, 52–81

[2] A. N. Borodin, “Raspredeleniya funktsionalov ot telegrafnogo protsessa i diffuzii s pereklyucheniyami”, Zap. nauchn. semin. POMI, 466, 2017, 38–53

[3] M. Kac, “On distribution of certain Wiener functionals”, Trans. Amer. Math. Soc., 65:1 (1949), 1–13 | DOI | MR | Zbl

[4] A. N. Borodin, Stochastic Processes, Birkhäuser, Cham, Switzerland, 2017 | Zbl

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

[6] G. Beitmen, A. Erdeii, Tablitsy integralnykh preobrazovanii, v. I, Nauka, M., 1969