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Huijie Qiao

Publications and source records attributed to Huijie Qiao.

At least 19 recordsLinked to original sources
arXiv2026

Averaging principles for nonautonomous multiscale stochastic Burgers equations with reflection

In this paper, we study averaging principles for nonautonomous multiscale stochastic Burgers equations with reflection. First, we derive a general averaging principle applicable to such equations under minimal assumptions. Subsequently, since the coefficients of the obtained averaged equation still depend on the small scaling parameter $\e$, we impose either periodic or asymptotic conditions on the coefficients, thereby obtain two distinct averaged equations whose coefficients are independent of $\e$ and establish two averaging principles. Stopping times and Khasminskii's time discretization schemes play an important role. Finally, a concrete example is provided to illustrate the applicability and validity of the theoretical results.

math.PR↗
arXiv2026

Large deviation principles for multiscale stochastic Burgers equations with reflection

This study investigates multiscale stochastic Burgers equations with reflection, wherein the slow component is modeled by a stochastic Burgers equation with reflection and the fast component by a stochastic reaction-diffusion equation with reflection. Using the weak convergence approach, we rigorously establish a large deviation principle for the slow component. Key technical tools include the penalization method, carefully constructed stopping times, and a refined adaptation of Khasminskii's classical time discretization scheme.

math.PR↗
arXiv2026

Averaging principles for nonautonomous multiscale McKean-Vlasov stochastic systems

This paper investigates a class of nonautonomous multiscale McKean-Vlasov stochastic systems. By leveraging the nonautonomous Poisson equation, we rigorously establish both strong and weak averaging principles, accompanied by explicit convergence rates. Notably, the coefficients of the averaging equations derived in the general case retain dependence on the scaling parameter $\varepsilon$. However, under the additional assumptions that the fast-scale coefficients are either asymptotically convergent or time-periodic, we demonstrate that the slow component converges, in the strong or weak sense, to averaging equations with coefficients independent of $\varepsilon$.

math.PR↗
arXiv2026

Small noise asymptotic behaviors for path-dependent multivalued McKean-Vlasov stochastic differential equations

This paper investigates the asymptotic behavior of path-dependent multivalued McKean-Vlasov stochastic differential equations perturbed by small noise. Specifically, we first establish a large deviation principle for such equations under non-Lipschitz coefficients by the weak convergence approach. Subsequently, we introduce an auxiliary equation and apply it to derive the moderate deviation principle. Finally, we construct another auxiliary equation and a limit equation, and prove the central limit theorem.

math.PR↗
arXiv2025

Large deviations for invariant measures of multivalued stochastic differential equations with jumps

This work focuses on multivalued stochastic differential equations with jumps. First, by employing the weak convergence approach, we establish the Freidlin-Wentzell uniform large deviation principle and the Dembo-Zeitouni uniform large deviation principle for these equations. Subsequently, based on these results, we derive both upper and lower bounds for the large deviations of invariant measures associated with the equations.

math.PR↗
arXiv2025

Large deviation principles for fully coupled multiscale multivalued stochastic systems

This study focuses on large deviation principles for fully coupled multiscale multivalued stochastic systems, in which the slow component is governed by a multivalued stochastic differential equation and the fast component is described by a general stochastic differential equation. First, we establish the large deviation principle for the slow component at any fixed time by leveraging viscosity solutions of second-order Hamilton-Jacobi-Bellman equations involving multivalued operators. Subsequently, we illustrate the theoretical results through a concrete example.

math.PR↗
arXiv2025

Asymptotic behaviors of multiscale multivalued stochastic systems with small noises

In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with small noises in the slow components, we prove an averaging principle in the strong convergence sense. Moreover, a convergence rate is given in a special case. Next, for these systems, we establish the large deviation principle by the weak convergence approach. Then for a special case the rate function is explicitly characterized. Finally, we explain our results by an example.

math.PR↗
arXiv2025

Large deviations of multiscale multivalued McKean-Vlasov stochastic systems

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we use a contractive mapping principle to establish the well-posedness for fully coupled multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Then for multiscale multivalued McKean-Vlasov stochastic systems with small noises, we prove a large deviation principle by a weak convergence approach. As a by-product, two averaging principles are obtained.

math.PR↗
arXiv2025

Averaging principles and central limit theorems for multiscale McKean-Vlasov stochastic systems

In this paper, we study a class of multiscale McKean-Vlasov stochastic systems where the entire system depends on the distribution of the fast component. First of all, by the Poisson equation method we prove that the slow component converges to the solution of the averaging equation in the $L^p$ ($p\geq 2$) space with the optimal convergence rate 1/2. Then a central limit theorem is established by tightness.

math.PR↗
arXiv2025

Asymptotic behaviors of multiscale McKean-Vlasov stochastic systems

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove that the slow component converges to the solution of the averaging equation in the $L^p$ ($p\geq 2$) space with the optimal convergence order $\frac12$. Then we establish a central limit theorem for these systems and derive the weak convergence rate using the Poisson equation technique and the regularity properties of the associated Cauchy problem.

math.PR↗
arXiv2025

Well-posedness for path-dependent multivalued McKean-Vlasov stochastic differential equations

This work concerns a type of path-dependent multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the well-posedness for path-dependent multivalued stochastic differential equations under the Lipschitz conditions. Then by constructing Lipschitz approximation sequences, we generalize the result to the case of the non-Lipschitz conditions. Finally, based on the obtained results, the well-posedness for path-dependent multivalued McKean-Vlasov stochastic differential equations under the non-Lipschitz conditions is established by iterating in distributions.

math.PR↗
arXiv2025

General large deviations and functional iterated logarithm law for multivalued McKean-Vlasov stochastic differential equations

In this paper, we present sufficient conditions and criteria to establish general large and moderate deviation principles for multivalued McKean-Vlasov stochastic differential equations (SDEs in short) by means of the weak convergence approach, under non-Lipschit assumptions on the coefficents of the equations. Furthermore, by applying the large deviation estimates we obtain the functional iterated logarithm law for the solutions of multivalued McKean-Vlasov SDEs.

math.PR↗
arXiv2025

Uniform large deviation principles and averaging principles for stochastic Burgers type equations with reflection

This work concerns about stochastic Burgers type equations with reflection. First of all, by means of the equicontinuous uniform Laplace principle, we prove the Freidlin-Wentzell uniform large deviation principle for these equations uniformly on bounded sets. Then based on this result, we establish the Dembo-Zeitouni uniform large deviation principle for these equations uniformly on compact sets. Finally, an averaging principle result for these equations is obtained through the time discretization approach.

math.PR↗
arXiv2024

Large deviations for generalized backward stochastic differential equations

This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential equations with reflecting boundaries under weak monotonicity conditions. Then based on the obtained result and the contraction principle, the large deviation principle for the generalized backward stochastic differential equations is proved. As a by-product, we obtain a limit result about parabolic partial differential equations with the nonlinear Neumann boundary conditions.

math.PR↗
arXiv2024

Path independence for the additive functionals of stochastic Volterra equations with singular kernels and Hölder continuous coefficients

In this paper, we are concerned with stochastic Volterra equations with singular kernels and Hölder continuous coefficients. We first establish the well-posedness of these equations by utilising the Yamada-Watanabe approach. Then, we aim to characterise the path-independence for additive functionals of these equations. The main challenge here is that the solutions of stochastic Volterra equations are not semimartingales nor Markov processes, thus the existing techniques for obtaining the path-independence of usual, semimartingale type stochastic differential equations are no longer applicable. To overcome this difficulty, we link the concerned stochastic Volterra equations to mild formulation of certain parabolic type stochastic partial differential equations, and further apply our previous results on the path-independence for stochastic evolution equations to get the desired result. Finally, as an important application, we consider a class of stochastic Volterra equations whose kernels are related with fractional Brownian motions and derive the path-independence of additive functionals for them.

math.PR↗
arXiv2024

Probabilistic approach to homogenization for a type of multivalued Dirichlet-Neumann problems

The work is about homogenization for a type of multivalued Dirichlet-Neumann problems. First, we prove an average principle for general multivalued stochastic differential equations in the weak sense. Then for general forward-backward coupled multivalued stochastic systems, the other average principle is presented. Finally, we apply the result to a type of multivalued Dirichlet-Neumann problems and investigate its homogenization.

math.PR↗
arXiv2023

Stability for multivalued McKean-Vlasov stochastic differential equations

The work concerns multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equations with non-Lipschitz coefficients. Then, the classical Itô's formula is extended to that for multivalued McKean-Vlasov stochastic differential equations. Finally, the asymptotic stability of second moments and the almost surely asymptotic stability for their solutions in terms of a Lyapunov function are shown.

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