arXiv subjects

Yuanping Cui

Publications and source records attributed to Yuanping Cui.

5 recordsLinked to original sources

arXiv2026

An explicit adaptive time-stepping scheme for superlinear stochastic diffusion systems

This paper develops an adaptive time-stepping Euler--Maruyama (EM) scheme for stochastic diffusion systems with superlinearly growing coefficients. The adaptive timestep is chosen according to the superlinear growth of both drift and diffusion coefficients. To prevent excessively small timesteps, a truncated EM scheme is employed as a backstop whenever the adaptive timestep falls below a prescribed threshold. By combining the stochastic analysis with the stopping time technique, we establish the strong convergence of the proposed method and obtain the optimal $1/2$-order strong convergence rate in the $L^q$-sense for $q>2$. {Finally, numerical experiments are carried out for stiff, nonstiff, and stochastic Lorenz systems to validate the theoretical findings. The results indicate that the proposed scheme achieves superior accuracy and performance compared to various fixed-step and adaptive alternatives.

math.NA↗

arXiv2024

Numerical approximation to the invariant measure of McKean-Vlasov stochastic differential equations

Inspired by the stochastic particle method, this paper develops an easily implementable explicit scheme for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. We prove that the numerical solution of the interacting particle system (IPS) attains the optimal uniform-in-time strong convergence rate of order 1/2, and that it faithfully captures the long-term dynamics of MV-SDEs, including moment boundedness, stability, and ergodicity. In particular, the existence and uniqueness of an exchangeable numerical invariant probability measure for the IPS are established via an appropriately constructed operator semigroup. Concerning the approximation of the invariant measure, we derive a non-asymptotic error bound between the distribution of the one-particle numerical solution and the marginal distribution of the IPS's invariant measure; By the uniform-in-time propagation of chaos, we further obtain an asymptotic error bound between the one-particle marginal of the IPS's numerical invariant measure and the exact invariant measure of the MV-SDE. Numerical experiments are provided to validate the theoretical results.

math.PR↗

arXiv2023

Strong convergence of multiscale truncated Euler-Maruyama method for super-linear slow-fast stochastic differential equations

This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler-Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.

math.NA↗

arXiv2023

Wolbachia invasion to wild mosquito population in stochastic environment

Releasing sterile Wolbachia-infected mosquitoes to invade wild mosquito population is a method of mosquito control. In this paper, a stochastic mosquito population model with Wolbachia invasion perturbed by environmental fluctuation is studied. Firstly, well-posedness, positivity and Markov-Feller property of solution for this model are proved. Then a group of sharp threshold-type conditions is provided to characterize the long-term behavior of the model, which pinpoints the almost necessary and sufficient conditions for persistence and extinction of Wolbachia-infected and uninfected mosquito populations. Especially, our results indicates that even the initial Wolbachia infection frequency is low, the Wolbachia invasion into wild mosquito population can be promoted by stochastic environmental fluctuations. Finally, some numerical experiments are carried out to support our theoretical results.

math.DS↗

arXiv2021

Explicit Numerical Approximations for McKean-Vlasov Neutral Stochastic Differential Delay Equations

This paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that the solution of MV-NSDDE exists and is unique. Then, we use a stochastic particle method, which is on the basis of the results about the propagation of chaos between particle system and the original MV-NSDDE, to deal with the approximation of the law. Furthermore, we construct the tamed Euler-Maruyama numerical scheme with respect to the corresponding particle system and obtain the rate of convergence. Combining propagation of chaos and the convergence rate of the numerical solution to the particle system, we get a convergence error between the numerical solution and exact solution of the original MV-NSDDE in the stepsize and number of particles.

math.PR↗