arXiv subjects

Vu Thi Hue

Publications and source records attributed to Vu Thi Hue.

3 recordsLinked to original sources

arXiv2026

Two-sided estimates of Lyapunov exponents for Milstein schemes of non-autonomous stochastic differential equations

The stabilising effect of multiplicative noise for stochastic differential equations, though counterintuitive, has been observed and investigated extensively in last decades. In practice, it is desirable to know if such stabilisation holds also for the discretised setting. In this paper, we address this problem by means of sharp upper and lower estimates for Lyapunov exponents of Milstein schemes for non-autonomous stochastic differential equations. These estimates provide precise large time behaviour in both almost sure and $p$-moment sense. In particular, our results show the preservation of stabilisation from the continuum setting to the discretised setting. One main idea of our analysis is to exploit the second order term concerning the stochastic noise from the Milstein scheme to obtain precise estimates for Taylor expansions of logarithmic and power functions.

math.NA↗

arXiv2026

Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms for Lévy-driven stochastic differential equations

We study the error between the exact solution and its Euler-Maruyama approximation in temporal-spatial Hölder-norms for Lévy-driven stochastic differential equations.

math.PR↗

arXiv2025

Sharp estimates for Lyapunov exponents of Milstein approximation of stochastic differential systems

The Milstein approximation with step size $Δt>0$ of the solution $(X, Y)$ to a two-by-two system of linear stochastic differential equations is considered. It is proved that when the solution of the underlying model is exponentially stable or exponentially blowing up at infinite time, these behaviours are preserved at the level of the Milstein approximate solution $\{(X_n, Y_n)\}$ in both the mean-square and almost-sure senses, provided sufficiently small step size $Δt$. This result is based on sharp estimates, from both above and below, of the discrete Lyapunov exponent. This type of sharp estimate for approximate solutions to stochastic differential equations seems to be first studied in this work. In particular, the proposed method covers the setting for linear stochastic differential equations as well as the $θ$-Milstein scheme's setting.

math.PR↗