Numerical preservation issues in stochastic dynamical systems by $ \vartheta $-methods

<p style='text-indent:20px;'>This paper analyzes conservation issues in the discretization of certain stochastic dynamical systems by means <inline-formula><tex-math id="M2">\begin{document}$ \vartheta $\end{document}</tex-math></inline-formula>-mehods. The analysis also takes into account effects estimation expected values Monte Carlo simulations. theoretical is supported a numerical evidence on given oscillator, inspired Duffing oscillator.</p>