Geodesic
On some random integral operators generated by an Arratia flow
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 8-18.

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

We study some properties of a random integral operator in $L_2( \mathbb{R})$ whose kernel is generated by a stationary point process related to an Arratia flow. To prove that this random operator is not bounded we estimate the rate of growth of the maximal amount of clusters in Arratia flow on intervals of unit length.
Keywords: Arratia flow, strong random operator, point process, stochastic flow. 
@article{THSP_2017_22_2_a1,
     author = {A. A. Dorogovtsev and Ia. A. Korenovska and E. V. Glinyanaya},
     title = {On some random integral operators generated by an {Arratia} flow},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {8--18},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a1/}
}
TY  - JOUR
AU  - A. A. Dorogovtsev
AU  - Ia. A. Korenovska
AU  - E. V. Glinyanaya
TI  - On some random integral operators generated by an Arratia flow
JO  - Teoriâ slučajnyh processov
PY  - 2017
SP  - 8
EP  - 18
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a1/
LA  - en
ID  - THSP_2017_22_2_a1
ER  - 
%0 Journal Article
%A A. A. Dorogovtsev
%A Ia. A. Korenovska
%A E. V. Glinyanaya
%T On some random integral operators generated by an Arratia flow
%J Teoriâ slučajnyh processov
%D 2017
%P 8-18
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a1/
%G en
%F THSP_2017_22_2_a1
A. A. Dorogovtsev; Ia. A. Korenovska; E. V. Glinyanaya. On some random integral operators generated by an Arratia flow. Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 8-18. http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a1/

[1] R. Arratia, Brownian motion on the line, PhD dissertation, Univ. Wisconsin, 1979 | MR

[2] A. A. Dorogovtsev, “Krylov-Veretennikov expansion for coalescing stochastic flows”, Commun. Stoch. Anal., 6:3 (2012), 421–435 | MR | Zbl

[3] A. A. Dorogovtsev, Measure-valued processes and stochastic flows, Institute of Mathematics of the NAS of Ukraine, Kiev, 2007 (Russian) | MR | Zbl

[4] A. A. Dorogovtsev, “Some remarks about Brownian flow with coalescence”, Ukr. Math. J., 57:10 (2005), 1327–1333 | DOI | MR | Zbl

[5] A. A. Dorogovtsev, Stochastic analysis and random maps in Hilbert space, VSP, Utrecht, 1994 | MR | Zbl

[6] A. A. Dorogovtsev, Ia. A. Korenovska, “Essential Sets for Random Operators Constructed from an Arratia Flow”, Communications on Stochastic Analysis, 11:3 (2017), 301–312 | DOI | MR

[7] A. A. Dorogovtsev, Ia. A. Korenovska, “Some random integral operators related to a point processes”, Theory of Stochastic Processes, 22 (38):1 (2017), 16–21 | MR | Zbl

[8] V. V. Fomichov, “The level-crossing intensity for the density of the image of the Lebesgue measure under the action of a Brownian stochastic flow”, Ukr. Math. J., 69:6 (2017), 803–822 (Russian) | MR

[9] L. R. G. Fontes, M. Isopi, C. M. Newman, K. Ravishankar, “The Brownian web”, Proc. Nat. Acad. Sciences, 99 (2002), 15888–15893 | DOI | MR | Zbl

[10] E. V. Glinyanaya, “Spatial Ergodicity of the Harris Flows”, Communications on Stochastic Analysis, 11:2 (2017), 223–231 | DOI | MR

[11] Ya. A. Korenovskaya, “Properties of Strong Random Operators Generated by the Arratia Flow”, Ukrainian Mathematical Journal, 69:2 (2017), 186–204 | DOI | MR

[12] G. Last, M. Penrose, Lectures on the Poisson Processes, Cambridge University Press, 2017 (to appear) | MR

[13] M. A. Lifshits, Gaussian random functions, Kluwer, Dordrecht, 1995 | MR | Zbl

[14] Y. Peres, P. Mörters, Brownian motion, Cambridge University Press, 2010 | MR | Zbl

[15] A. V. Skorokhod, Random linear operators, D.Reidel Publishing Company, Dordrecht, Holland, 1983 | MR