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Statistical analysis of diffusion systems with invariants. / Averina, Tatiana A.; Karachanskaya, Elena V.; Rybakov, Konstantin A.

In: Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 33, No. 1, 23.02.2018, p. 1-13.

Research output: Contribution to journal › Article › peer-review

Harvard

Averina, TA, Karachanskaya, EV & Rybakov, KA 2018, 'Statistical analysis of diffusion systems with invariants', Russian Journal of Numerical Analysis and Mathematical Modelling, vol. 33, no. 1, pp. 1-13. https://doi.org/10.1515/rnam-2018-0001

APA

Averina, T. A., Karachanskaya, E. V., & Rybakov, K. A. (2018). Statistical analysis of diffusion systems with invariants. Russian Journal of Numerical Analysis and Mathematical Modelling, 33(1), 1-13. https://doi.org/10.1515/rnam-2018-0001

Vancouver

Averina TA, Karachanskaya EV, Rybakov KA. Statistical analysis of diffusion systems with invariants. Russian Journal of Numerical Analysis and Mathematical Modelling. 2018 Feb 23;33(1):1-13. doi: 10.1515/rnam-2018-0001

Author

Averina, Tatiana A. ; Karachanskaya, Elena V. ; Rybakov, Konstantin A. / Statistical analysis of diffusion systems with invariants. In: Russian Journal of Numerical Analysis and Mathematical Modelling. 2018 ; Vol. 33, No. 1. pp. 1-13.

BibTeX

@article{297dff494c80452f8d4c102c2f3399ff,
title = "Statistical analysis of diffusion systems with invariants",
abstract = "The aim of the paper is the construction and numerical solution of stochastic differential equations whose trajectories are located on a given smooth manifold with probability 1. Second order cylindrical surfaces, i.e., elliptic, hyperbolic, and parabolic cylinders serve as examples of such manifolds for the tree-dimensional space (the phase space is two-dimensional). Classes of stochastic differential equations are constructed for these surfaces and linear equations with multiplicative noise are marked in these classes. The results of modelling were used to estimate the deviations of numerical solutions from the manifold. A comparative analysis of considered examples was carried out for accuracy of eight numerical solution methods for stochastic differential equations.",
keywords = "First integral, Invariant, Numerical method, Random process, Stochastic differential equation",
author = "Averina, {Tatiana A.} and Karachanskaya, {Elena V.} and Rybakov, {Konstantin A.}",
year = "2018",
month = feb,
day = "23",
doi = "10.1515/rnam-2018-0001",
language = "English",
volume = "33",
pages = "1--13",
journal = "Russian Journal of Numerical Analysis and Mathematical Modelling",
issn = "0927-6467",
publisher = "Walter de Gruyter GmbH",
number = "1",

}

RIS

TY - JOUR

T1 - Statistical analysis of diffusion systems with invariants

AU - Averina, Tatiana A.

AU - Karachanskaya, Elena V.

AU - Rybakov, Konstantin A.

PY - 2018/2/23

Y1 - 2018/2/23

N2 - The aim of the paper is the construction and numerical solution of stochastic differential equations whose trajectories are located on a given smooth manifold with probability 1. Second order cylindrical surfaces, i.e., elliptic, hyperbolic, and parabolic cylinders serve as examples of such manifolds for the tree-dimensional space (the phase space is two-dimensional). Classes of stochastic differential equations are constructed for these surfaces and linear equations with multiplicative noise are marked in these classes. The results of modelling were used to estimate the deviations of numerical solutions from the manifold. A comparative analysis of considered examples was carried out for accuracy of eight numerical solution methods for stochastic differential equations.

AB - The aim of the paper is the construction and numerical solution of stochastic differential equations whose trajectories are located on a given smooth manifold with probability 1. Second order cylindrical surfaces, i.e., elliptic, hyperbolic, and parabolic cylinders serve as examples of such manifolds for the tree-dimensional space (the phase space is two-dimensional). Classes of stochastic differential equations are constructed for these surfaces and linear equations with multiplicative noise are marked in these classes. The results of modelling were used to estimate the deviations of numerical solutions from the manifold. A comparative analysis of considered examples was carried out for accuracy of eight numerical solution methods for stochastic differential equations.

KW - First integral

KW - Invariant

KW - Numerical method

KW - Random process

KW - Stochastic differential equation

UR - http://www.scopus.com/inward/record.url?scp=85042619036&partnerID=8YFLogxK

U2 - 10.1515/rnam-2018-0001

DO - 10.1515/rnam-2018-0001

M3 - Article

AN - SCOPUS:85042619036

VL - 33

SP - 1

EP - 13

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 1

ER -

ID: 10426615