2019
Том 71
№ 11

All Issues

Chernega P. P.

Articles: 2
Article (Russian)

Levy Downcrossing Theorem for the Arratia Flow

Chernega P. P.

↓ Abstract

Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 261-271

We study the total number of downcrossings of a fixed strip by the trajectories of a continuum system of particles from the Arratia flow. We prove the convergence of the product of the strip width by the total number of downcrossings of the strip to the total local time for the Arratia flow. This statement is an analog of the well-known Levy downcrossing theorem for a Wiener process.

Article (Russian)

Local time at zero for arratia flow

Chernega P. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 542-556

We study the Arratia flow $x(u,t)$. We prove that $x(\cdot,t)$ is a Markov process whose phase space is a certain subset $K$ of the Skorokhod space. We introduce the notion of total local time at zero for the Arratia flow. We prove that it is an additive, nonnegative, continuous functional of the flow and calculate its characteristic.