Open AccessNumerical preservation issues in stochastic dynamical systems by $ \vartheta $-methods
Author(s) -
Raffaele D’Ambrosio,
Stefano Di Giovacchino
Publication year - 2022
Publication title -
journal of computational dynamics
Language(s) - English
Resource type - Journals
eISSN - 2158-2505
pISSN - 2158-2491
DOI - 10.3934/jcd.2021023
Subject(s) - discretization , mathematics , stochastic process , monte carlo method , numerical analysis , duffing equation , dynamical systems theory , statistical physics , physics , mathematical analysis , statistics , quantum mechanics , nonlinear system
This paper analyzes conservation issues in the discretization of certain stochastic dynamical systems by means of stochastic \begin{document}$ \vartheta $\end{document} -mehods. The analysis also takes into account the effects of the estimation of the expected values by means of Monte Carlo simulations. The theoretical analysis is supported by a numerical evidence on a given stochastic oscillator, inspired by the Duffing oscillator.