**MSC2010** 37M10

### Kinetic equation for simulation of non-stationary non-equidistant time-series

#### L. V. Klochkova^{1}, Yu. N. Orlov^{2}, R. V. Pleshakov^{3}

Annotation | We obtain kinetic equation for the sample distribution function of the time series with values generated by non-stationary flow of events. In many practically observed time series unsteadiness is due to random switching from one random process to another. In these cases the attachments are filtered; it allows to select a stationary component of series. A model is proposed to describe the evolution of pollution levels in the city. In this model a sequence of time intervals between random events, which are the moments of pollutants' emission into the atmosphere, forms a non-stationary time series. Software package for calculating statistics that determine the evolution of the sampling distribution at a certain time interval is described. The conversion of these statistics from sample size to the time interval is implemented. The equation of their distributions' evolution in terms of empirical Liouville equation is obtained. |
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Keywords | sample distribution function, non-equidistant time series, Liouville equation, non-stationary flow of events |

^{1}**Ludmila V. Klochkova**, Senior Researcher, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4, Miusskaya sq., Moscow 125047, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0003-3973-3909, klud2015@mail.ru

^{2}**Yuriy N. Orlov**, Professor, Head of the Department, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4, Miusskaya sq., Moscow 125047, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-9114-0436, ov3159f@yandex.ru

^{3}**Ruslan V. Pleshakov**, Postgraduate Student, Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4, Miusskaya sq., Moscow 125047, Russia), ORCID: http://orcid.org/0000-0001-5368-4416, ruslanplkv@gmail.com

**Citation**: L. V. Klochkova, Yu. N. Orlov, R. V. Pleshakov, "[Kinetic equation for simulation of non-stationary non-equidistant time-series]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:1 (2018) 78–87 (In Russian)

**DOI** 10.15507/2079-6900.20.201801.78-87