arXiv subjects

Chenggui Yuan

Publications and source records attributed to Chenggui Yuan.

At least 19 recordsLinked to original sources

arXiv2026

Strong solutions and sharp Euler--Maruyama approximations for SDEs with Lebesgue--Dini drift

We investigate the strong approximation of stochastic differential equations whose drift is square-integrable in time and Dini continuous in space, while the diffusion coefficient is non-constant and uniformly elliptic. Using a refined It\^{o}--Tanaka trick combined with parabolic regularity estimates, we first establish strong well-posedness and the stochastic flow property. Under additional Lipschitz regularity of the diffusion matrix, we then analyze a polygonal-type Euler--Maruyama scheme and prove the strong error estimate \[ \Big\|\sup_{0\le t\le1}|X_t-X_t^n|\Big\|_{L^p(\Omega)} \le C n^{-\frac12}\log(n)^{\frac32}, \quad p\ge2. \] We further show that this rate is sharp: even under smooth and uniformly elliptic diffusion coefficients with vanishing drift, the convergence order $1/2$ cannot be improved. These results provide the first sharp quantitative strong convergence estimates in a Lebesgue--Dini drift framework.

math.PR↗

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

Large Deviation Principle for Neutral Type Mckean-Vlasov Stochastic Differential Equations

This paper investigates neutral-type McKean-Vlasov stochastic differential equations in which the drift and diffusion coefficients depend on both the segment process and its distribution. Under a one-sided Lipschitz condition on the drift coefficient, we establish a Freidlin-Wentzell-type large deviation principle for the solution process by using the extended contraction principle combined with an exponential approximation technique. Our results extend existing large deviation principles for McKean-Vlasov equations to the neutral case.

math.PR↗

arXiv2025

The ergodicity of nonlinear McKean-Vlasov stochastic differential equations with common noise

This paper focuses on the ergodicity of McKean-Vlasov (MV) stochastic differential equations (SDEs) with common noise (wCN), where coefficients depend on both the state and the measure. A major challenge in this setting is that the underlying Markov operator loses the semigroup property, precluding standard ergodic analyses. To circumvent this issue, we lift the system by considering the joint flow of the solution and its conditional distribution. We first construct a semigroup associated with the measure pair of the solution and its conditional distribution. Under polynomial growth conditions, we prove the existence and uniqueness of the invariant measure for the lifted system by a coupling method and obtain an explicit exponential convergence rate. We subsequently derive the strong law of large numbers by a decoupling approach. Building on these results, we establish the uniform-in-time propagation of chaos for the associated mean-field interacting particle system. Furthermore, we establish the convergence of the distribution of a single particle and the empirical measure of the particle system to the marginals of the invariant measure. Finally, illustrative examples are provided to verify the theoretical findings.

math.PR↗

arXiv2025

A new proof on quasilinear Schr\"{o}dinger equations with prescribed mass and combined nonlinearities

In this work, we study the quasilinear Schr\"{o}dinger equation \begin{equation*} \aligned -\Delta u-\Delta(u^2)u=|u|^{p-2}u+|u|^{q-2}u+\lambda u,\,\, x\in\R^N, \endaligned \end{equation*} under the mass constraint \begin{equation*} \int_{\R^N}|u|^2\text{d}x=a, \end{equation*} where $N\geq2$, $2 0$ is a given mass and $\lambda$ is a Lagrange multiplier. As a continuation of our previous work (Chen et al., 2025, arXiv:2506.07346v1), we establish some results by means of a suitable change of variables as follows: \begin{itemize} \item[{\bf(i) }] {\bf qualitative analysis of the constrained minimization}\\ For $2 0$; \end{itemize} \begin{itemize} \item[{\bf(ii)}]{\bf existence of two radial distinct normalized solutions}\\ For $2<p<2+\frac{4}{N}<4+\frac{4}{N}<q<22^*$, we obtain a local minimizer under the normalized constraint;\\ For $2<p<2+\frac{4}{N}<4+\frac{4}{N}<q\leq2^*$, we obtain a mountain pass type normalized solution distinct from the local minimizer. \end{itemize} Notably, the second result {\bf (ii)} resolves the open problem {\bf(OP1)} posed by (Chen et al., 2025, arXiv:2506.07346v1). Unlike previous approaches that rely on constructing Palais-Smale-Pohozaev sequences by [Jeanjean, 1997, Nonlinear Anal. {\bf 28}, 1633-1659], we obtain the mountain pass solution employing a new method, which lean upon the monotonicity trick developed by (Chang et al., 2024, Ann. Inst. H. Poincar\'{e} C Anal. Non Lin\'{e}aire, {\bf 41}, 933-959). We emphasize that the methods developed in this work can be extended to investigate the existence of mountain pass-type normalized solutions for other classes of quasilinear Schr\"{o}dinger equations.

math.AP↗

arXiv2025

On the infinite time horizon approximation for L\'evy-driven McKean-Vlasov SDEs with common noise

In this work, we establish the existence and uniqueness of solutions to McKean-Vlasov stochastic differential equations (SDEs) driven by L\'evy processes with common noise on an infinite time horizon, by means of a contraction mapping principle in the space of probability measures. In addition, we analyse the propagation of chaos for L\'evy-driven McKean-Vlasov SDEs in the presence of common noise.

math.PR↗

arXiv2025

The Euler-Maruyama method for SDEs with low-regularity drift

We study the strong $L^p$-convergence rates of the Euler-Maruyama method for stochastic differential equations driven by Brownian motion with low-regularity drift coefficients. Specifically, the drift is assumed to be in the Lebesgue-H\"{o}lder spaces $L^q([0,T]; {\mathcal C}_b^\alpha({\mathbb R}^d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),\infty]$. For every $p\geq 2$, by using stochastic sewing and/or the It\^{o}-Tanaka trick, we obtain the $L^p$-convergence rates: $(1+\alpha)/2$ for $q\in [2,\infty]$ and $(1-1/q)$ for $q\in (2/(1+\alpha),2)$. Moreover, we prove that the unique strong solution can be constructed via the Picard iteration.

math.PR↗

arXiv2025

The LDP of McKean-Vlasov stochastic differential equations with H\"{o}lder continuous conditions and integrable conditions

In this paper, we first study the large deviation principle (LDP) for non-degenerate McKean-Vlasov stochastic differential equations (MVSDEs) with H\"{o}lder continuous drifts by using Zvonkin's transformation. When the drift only satisfies H\"{o}lder condition, the skeleton equation may have multiple solutions. Among these solutions, we find one that ensures the MVSDEs satisfy the LDP. Moreover, we introduce a new definition for the rate function that reduces to traditional rate function if the drift satisfies the Lipschitz condition. Secondly, we study the LDP for degenerate MVSDEs with H\"{o}lder continuous drifts.

math.PR↗

arXiv2025

Path-Distribution Dependent SDEs: Well-Posedness and Asymptotic Log-Harnack Inequality

We consider stochastic differential equations on $\mathbb R^d$ with coefficients depending on the path and distribution for the whole history. Under a local integrability condition on the time-spatial singular drift, the well-posedness and Lipschitz continuity in initial values are proved, which is new even in the distribution independent case. Moreover, under a monotone condition, the asymptotic log-Harnack inequality is established, which extends the corresponding result of [5] derived in the distribution independent case.

math.PR↗

arXiv2025

Propagation of chaos and Razumikhin theorem for the nonlinear McKean-Vlasov SFDEs with common noise

As the limit equations of mean-field particle systems perturbed by common environmental noise, the McKean-Vlasov stochastic differential equations with common noise have received a lot of attention. Moreover, past dependence is an unavoidable natural phenomenon for dynamic systems in life sciences, economics, finance, automatic control, and other fields. Combining the two aspects above, this paper delves into a class of nonlinear McKean-Vlasov stochastic functional differential equations (MV-SFDEs) with common noise. The well-posedness of the nonlinear MV-SFDEs with common noise is first demonstrated through the application of the Banach fixed-point theorem. Secondly, the relationship between the MV-SFDEs with common noise and the corresponding functional particle systems is investigated. More precisely, the conditional propagation of chaos with an explicit convergence rate and the stability equivalence are studied. Furthermore, the exponential stability, an important long-time behavior of the nonlinear MV-SFDEs with common noise, is derived. To this end, the It\^o formula involved with state and measure is developed for the MV-SFDEs with common noise. Using this formula, the Razumikhin theorem is proved, providing an easy-to-implement criterion for the exponential stability. Lastly, an example is provided to illustrate the result of the stability.

math.PR↗

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

Long Time $\W_0$-$\widetilde{\W}_1$ type Propagation of Chaos for Mean Field Interacting Particle System

In this paper, a general result on the long time $\W_0$-$\widetilde{\W}_1$ type propagation of chaos, propagation of chaos with regularization effect, for mean field interacting particle system driven by L\'{e}vy noise is derived, where $\W_0$ is one half of the total variation distance while $\widetilde{\W}_1$ is the $L^1$-Wasserstein distance. By using the method of coupling, the general result is applied to mean field interacting particle system driven by multiplicative Brownian motion and additive $\alpha(\alpha>1)$-stable noise respectively, where the non-interacting drift is assumed to be dissipative in long distance and the initial distribution of interacting particle system converges to that of the limit equation in $\widetilde{\W}_1$.

math.PR↗

arXiv2023

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↗

arXiv2023

The delay feedback control for the McKean-Vlasov stochastic differential equations with common noise

Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean-Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of delay feedback control mechanisms. The aim of this paper is to design delay feedback control functions of the system state such that the controlled system to be boundedness in infinite horizon and further exponentially stable in the mean square. The designed controller, which depends only on the system state is easier to implement than that in [27] which was designed to depend on both system state and measure. The existence and uniqueness of the global solution of the controlled system is proved. The It\^o formula with respect to both state and measure is derived. The proposed delay feedback control strategies are rendered viable for effective stabilization of MV-SDEs with common noise. Furthermore, the moment Lyapunov exponent, which is intricately linked to the time delays, is meticulously estimated.

math.PR↗

arXiv2023

Multilevel Monte Carlo EM scheme for MV-SDEs with small noise

In this paper, we estimate the variance of two coupled paths derived with the Multilevel Monte Carlo method combined with the Euler Maruyama discretization scheme for the simulation of McKean-Vlasov stochastic differential equations with small noise. The result often translates into a more efficient method than the standard Monte Carlo method combined with algorithms tailored to the small noise setting.

math.PR↗

arXiv2023

Stochastic equations with low regularity drifts

By using the It\^{o}-Tanaka trick, we prove the unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular drifts in low regularity Lebesgue-H\"{o}lder space $L^q(0,T;{\mathcal C}_b^\alpha({\mathbb R}^d))$ with $\alpha\in(0,1)$ and $q\in (2/(1+\alpha),2$). As applications, we show the unique weak and strong solvability for stochastic transport equations driven by the low regularity drift with $q\in (4/(2+\alpha),2$) as well as the local Lipschitz estimate for stochastic strong solutions.

math.PR↗

arXiv2023

Large deviation for slow-fast McKean-Vlasov stochastic differential equations driven by fractional Brownian motions and Brownian motions

In this article, we consider slow-fast McKean-Vlasov stochastic differential equations driven by Brownian motions and fractional Brownian motions. We give a definition of the large deviation principle (LDP) on the product space related to Brownian motion and fractional Brownian motion, which is different from the traditional definition for LDP. Under some proper assumptions on coefficients, LDP is investigated for this type of equations by using the weak convergence method.

math.PR↗

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↗