arXiv subjects

Ruchun Zuo

Publications and source records attributed to Ruchun Zuo.

3 recordsLinked to original sources

arXiv2026

A diffusion time-changed stochastic SIS epidemic model: well-posedness, long-time behavior, and numerical approximation

In this paper, we propose and analyze a diffusion time-changed susceptible-infected-susceptible (SIS) epidemic model driven by time-changed Brownian motion. We prove that the proposed model admits a unique global positive solution for any initial value in $(0,N)$. The extinction and persistence of the disease are then investigated. To approximate the diffusion time-changed SIS model, we construct a positivity-preserving logarithmic Euler-Maruyama (LEM) method. Assuming that the time-changed is given by the inverse of a standard $α$-stable subordinator with $α\in(0,1)$, we prove that the numerical solution converges strongly to the exact solution with order $α$. Finally, numerical experiments are provided to confirm the predicted convergence rates and illustrate the positivity-preserving property of the proposed method.

math.NA↗

arXiv2026

Parameter-related strong convergence rates of Euler-type methods for time-changed stochastic differential equations

An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz condition.The theoretical analysis is then extended to the truncated Euler--Maruyama method, proving its strong convergence under relaxed Khasminskii-type conditions.Under suitable conditions, the strong convergence orders are explicitly shown to be close to $α/2$, where $α\in (0,1)$ is the parameter of the time-change process.These results are significantly different from existing works using random step sizes, which typically preserve the classical convergence order of $1/2$.Numerical simulations are provided to demonstrate the theoretical findings.

math.NA↗

arXiv2023

A Milstein-type method for highly non-linear non-autonomous time-changed stochastic differential equations

A Milstein-type method is proposed for some highly non-linear non-autonomous time-changed stochastic differential equations (SDEs). The spatial variables in the coefficients of the time-changed SDEs satisfy the super-linear growth condition and the temporal variables obey some Hölder's continuity condition. The strong convergence in the finite time is studied and the convergence order is obtained.

math.NA↗