Statistical analysis of diffusion systems with invariants

Tatiana A. Averina, Elena V. Karachanskaya, Konstantin A. Rybakov

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalRussian Journal of Numerical Analysis and Mathematical Modelling
Issue number1
Publication statusPublished - 23 Feb 2018


  • First integral
  • Invariant
  • Numerical method
  • Random process
  • Stochastic differential equation


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