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Digital
Library of the European Council for Modelling
and Simulation |
Title: |
Nonstationary Stochastic
Motion Modeling By Dynamical Systems |
Authors: |
Yurii
N. Orlov, Alexey A. Kislitsyn |
Published in: |
(2019). ECMS 2019
Proceedings Edited by: Mauro Iacono, Francesco Palmieri, Marco Gribaudo,
Massimo Ficco, European Council for Modeling and Simulation. DOI: http://doi.org/10.7148/2019 ISSN:
2522-2422 (ONLINE) ISSN:
2522-2414 (PRINT) ISSN:
2522-2430 (CD-ROM) 33rd International ECMS Conference on
Modelling and Simulation,
Caserta, Italy, June 11th – June 14th, 2019 |
Citation
format: |
Yurii N. Orlov, Alexey A. Kislitsyn (2019). Nonstationary Stochastic Motion Modeling By Dynamical Systems, ECMS 2019 Proceedings Edited by: Mauro Iacono, Francesco Palmieri, Marco Gribaudo, Massimo Ficco European Council for Modeling and Simulation. doi: 10.7148/2019-0466 |
DOI: |
https://doi.org/10.7148/2019-0466 |
Abstract: |
In this paper
we discuss two aspects of kinetic approach for time series modeling in terms
of dynamical system. One method is based on the interpretation of kinetic
equation for empirical distribution function density as a reduced description
of statistical mechanics for appropriate dynamical system. For example, if
distribution function density is satisfied to Liouville equation with some
velocity, then this velocity can be treated as an average velocity of
particle in phase space. The second method is based on the so-called Chernoff
theorem from the group theory. According to the consequence from this theorem
some iteration procedure exists for construction of group or semigroup, which
is equivalent in some sense to average shift generator over the trajectory of
appropriate dynamical system. Connection between these two methods enables us
to construct a strict approach to nonstationary time series modeling with
non-parametric estimation of statistical properties of corresponding sample
distribution function. Also the notion of Chernoff-equivalent semigroup can
be used for the calculation optimization procedure. |
Full
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