Ergodicity with respect to the spatial variable of discrete-time stochastic flows
DOI:
https://doi.org/10.15407/dopovidi2015.08.013Keywords:
discrete-time stochastic flows, ergodicity, stationary processesAbstract
We consider a discrete-time flow of particles in the random environment and investigate spatial properties for such flow at a fixed moment of time. Results about the stationarity and ergodicity of the flow are obtained.
Downloads
References
Norris J.R. Ann. Appl. Probab., 1999, 9: 78–109. https://doi.org/10.1214/aoap/1029962598
Zirbel C. L., Cinlar E. Adv. Appl. Prob., 1996, 28, No 1: 53–74. https://doi.org/10.1017/S0001867800027282
Arratia R. Coalescing Brownian motions on the line, Madison: University of Wisconsin–Madison, 1979.
Harris T.E. Stochastic Processes and their Applications, 1984, 17, No 2: 187–210. https://doi.org/10.1016/0304-4149(84)90001-2
Le Jan Y., Raimond O. Ann. Probab., 2004, 32, No 2: 1247–1315. https://doi.org/10.1214/009117904000000207
Kunita H. Stochastic flows and stochastic differential equations, Cambridge Studies in Advanced Mathematics, Vol. 24, Cambridge: Cambridge University Press, 1997.
Kraichnan R. Turbulence in Fluid flows, IMA Volumes in Mathematics and its Applications, Vol. 55, New York: Springer, 1993: 73–86. https://doi.org/10.1007/978-1-4612-4346-5_5
Dorogovtsev A.A. Measure-Valued Processes and Stochastic Flows, Institute of Mathematics of the NAS of Ukraine, 2007 (in Russian).
Konarovskii V.V. System of interaction particles with changeable mass, PhD dissertation, Institute of Mathematics of the NAS of Ukraine, Kyiv, 2011 (in Ukrainian).
Mohammed S.-E.A., Scheutzow M.K.R. Ann. Probab, 1998, 26, No 1: 56–77. https://doi.org/10.1214/aop/1022855411
Warren J., Watanabe S. On spectra of noises associated with Harris flows, arXiv: math/0307287, 2003.
Kuznetsov D. F. Stochastic Differential Equations: Theory and Practice of Numerical Analysis, Saint-Petersburg: Polytechnic Univ., 2010 (in Russian).
Nishenko I. I. Theory Stoch.Process, 2011, 17, No 1: 70–78.
Kornfeld I. P., Sinai Ya.G., Fomin S.V. Ergodic Theory, Moscow: Nauka, 1980 (in Russian).
Rozanov Yu.A. Stationary Random Processes, Moscow: Nauka, 1990 (in Russian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
