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Shuaibin Gao

Publications and source records attributed to Shuaibin Gao.

13 recordsLinked to original sources
arXiv2026

McKean-Vlasov stochastic differential equations with super-linear measure arguments: well-posedness and propagation of chaos

This paper studies McKean-Vlasov stochastic differential equations (MVSDEs) whose drift coefficients grow super-linearly in both state variables and measure arguments, and whose diffusion coefficients exhibit super-linear growth in the state variables. By constructing an Euler-like sequence, we establish the strong well-posedness of such MVSDEs under a locally monotone condition. Furthermore, the propagation of chaos is studied on both finite and infinite horizons, demonstrating convergence of the interacting particle system to the corresponding non-interacting system. To illustrate the rationality of the theoretical results, we provide examples whose drifts contain the high powers and multiple integrals of distributions, with numerical simulations presented in Section 6.

math.PR↗
arXiv2025

The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons

This paper is dedicated to investigating the adaptive Euler-Maruyama (EM) schemes for the approximation of McKean-Vlasov stochastic differential equations (SDEs) with common noise. When the drift and diffusion coefficients both satisfy the superlinear growth conditions, the $L^p$ convergence rates in finite and infinite horizons are revealed, which reacts to the particle number and step size. Subsequently, there is an illustration of the theory results by means of two numerical examples.

math.NA↗
arXiv2025

Propagation of chaos in infinite horizon and numerical stability for stochastic McKean-Vlasov equations

This paper focuses on the numerical stability of stochastic McKean-Vlasov equations (SMVEs) via the stochastic particle method. Firstly, the long-time propagation of chaos in the mean-square sense is obtained, and the almost sure propagation in infinite horizon is also proved. Next, when the coefficients satisfy linear growth conditions, the mean-square and almost sure exponential stabilities of the Euler-Maruyama (EM) scheme associated with the corresponding interacting particle system are shown through an ingenious manipulation of empirical measure. Then, for the case that the state variables in drift and diffusion are both superlinear, the mean-square exponential stability of the backward EM scheme for the interacting system is achieved without the particle corruption, which is a novel conclusion. Moreover, under the linear growth condition on the diffusion coefficient, the almost sure stability of the backward EM scheme is studied. Combining these assertions enables the numerical solutions to reproduce the stabilities of the original SMVEs. The examples, including a feedback control problem and a stochastic opinion dynamics model, are provided to demonstrate the importance of theoretical analysis of numerical stability.

math.NA↗
arXiv2024

Numerical scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion

This paper focuses on the numerical scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter $H\in (0,1/2)\cup (1/2,1)$. The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial delay terms are proved by exploting the Banach fixed point theorem. Then the propagation of chaos between interacting particle system and non-interacting system in $\mathcal{L}^p$ sense is shown. We find that even if the delay term satisfies the polynomial growth condition, the unmodified classical Euler-Maruyama scheme still can approximate the corresponding interacting particle system without the particle corruption. The convergence rates are revealed for $H\in (0,1/2)\cup (1/2,1)$. Finally, as an example that closely fits the original equation, a stochastic opinion dynamics model with both extrinsic memory and intrinsic memory is simulated to illustrate the plausibility of the theoretical result.

math.NA↗
arXiv2024

The truncated EM scheme for multiple-delay SDEs with irregular coefficients and application to stochastic volatility model

This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially Hölder continuous drifts and locally Hölder continuous diffusion coefficients. To handle with the superlinear terms in coefficients, the truncated Euler-Maruyama scheme is employed. Under the given conditions, the convergence rates at time $T$ in both $\mathcal{L}^{1}$ and $\mathcal{L}^{2}$ senses are shown by virtue of the Yamada-Watanabe approximation technique. Moreover, the convergence rates over a finite time interval $[0,T]$ are also obtained. Additionally, it should be noted that the convergence rates will not be affected by the number of delay variables. Finally, we perform the numerical experiments on the stochastic volatility model to verify the reliability of the theoretical results.

math.NA↗
arXiv2023

The randomized Milstein scheme for stochastic Volterra integral equations with weakly singular kernels

This paper focuses on the randomized Milstein scheme for approximating solutions to stochastic Volterra integral equations with weakly singular kernels, where the drift coefficients are non-differentiable. An essential component of the error analysis involves the utilization of randomized quadrature rules for stochastic integrals to avoid the Taylor expansion in drift coefficient functions. Finally, we implement the simulation of multiple singular stochastic integral in the numerical experiment by applying the Riemann-Stieltjes integral.

math.NA↗
arXiv2023

Convergence rate in $\mathcal{L}^p$ sense of tamed EM scheme for highly nonlinear neutral multiple-delay stochastic McKean-Vlasov equations

This paper focuses on the numerical scheme of highly nonlinear neutral multiple-delay stohchastic McKean-Vlasov equation (NMSMVE) by virtue of the stochastic particle method. First, under general assumptions, the results about propagation of chaos in $\mathcal{L}^p$ sense are shown. Then the tamed Euler-Maruyama scheme to the corresponding particle system is established and the convergence rate in $\mathcal{L}^p$ sense is obtained. Furthermore, combining these two results gives the convergence error between the objective NMSMVE and numerical approximation, which is related to the particle number and step size. Finally, two numerical examples are provided to support the finding.

math.NA↗
arXiv2022

Mean-square convergence and stability of the backward Euler method for stochastic differential delay equations with highly nonlinear growing coefficients

Over the last few decades, the numerical methods for stochastic differential delay equations (SDDEs) have been investigated and developed by many scholars. Nevertheless, there is still little work to be completed. By virtue of the novel technique, this paper focuses on the mean-square convergence and stability of the backward Euler method (BEM) for SDDEs whose drift and diffusion coefficients can both grow polynomially. The upper mean-square error bounds of BEM are obtained. Then the convergence rate, which is one-half, is revealed without using the moment boundedness of numerical solutions. Furthermore, under fairly general conditions, the novel technique is applied to prove that the BEM can inherit the exponential mean-square stability with a simple proof. At last, two numerical experiments are implemented to illustrate the reliability of the theories.

math.NA↗
arXiv2022

An explicit Euler method for McKean-Vlasov SDEs driven by fractional Brownian motion

In this paper, we establish the theory of chaos propagation and propose an Euler-Maruyama scheme for McKean-Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst exponent $H \in (0,1)$. Meanwhile, upper bounds for errors in the Euler method is obtained. A numerical example is demonstrated to verify the theoretical results.

math.NA↗
arXiv2021

The truncated $θ$-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

This paper focuses on the strong convergence of the truncated $θ$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate, which is close to one, is given under the weaker assumption than the monotone condition. To verify our theoretical findings, we present a numerical example.

math.NA↗
arXiv2021

Stabilization of stochastic McKean-Vlasov equations with feedback control based on discrete-time state observation

In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic stability and exponential stability in mean square for the solution of the controlled systems are obtained. Since the distribution of solution is difficult to be observed, we study the corresponding particle system which can be observed for the feedback control. We prove that the exponential stability of control system is equivalent to the the exponential stability of the corresponding particle system. Finally, an example is provided to show the effectiveness of the theory.

math.PR↗
arXiv2020

The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is proposed, which numerical solutions are bounded and converge to the exact solutions in qth moment for q>0. Furthermore, the 1/2 order convergent rate is yielded. Under the Khasminskii-type condition, a more precise TEM scheme is given, which numerical solutions are exponential stable in mean square and P-1. Finally, several numerical experiments are carried out to illustrate our results.

math.NA↗