182 citations · 1.5k across the 227 of their papers we have counts for
30 papers · 1 filter
Well-posedness and averaging principle for Lévy-type McKean-Vlasov stochastic differential equations under local Lipschitz conditions
Ying Chao, Jinqiao Duan, Ting Gao +1
In this paper, we investigate a class of McKean-Vlasov stochastic differential equations under Lévy-type perturbations. We first establish the existence and uniqueness theorem for…
Kantorovich-Rubinstein Distance and Approximation for Non-local Fokker-Planck Equations
Ao Zhang, Jinqiao Duan
This work is devoted to studying complex dynamical systems under non-Gaussian fluctuations. We first estimate the Kantorovich-Rubinstein distance for solutions of non-local Fokker-…
Stochastic turbulence for Burgers equation driven by cylindrical Lévy process
Shenglan Yuan, Dirk Blömker, Jinqiao Duan
This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodi…
Homogenization of Dissipative Hamiltonian Systems under Lévy Fluctuations
Zibo Wang, Li Lv, Jinqiao Duan
This work is devoted to deriving small mass limiting equation for a class of Hamiltonian systems with multiplicative Lévy noise. Derivation of the limiting equation depends on the…
Large Deviations for SDE driven by Heavy-tailed Lévy Processes
Wei Wei, Qiao Huang, Jinqiao Duan
We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed Lévy processes. These heavy-tailed Lévy…
Onsager-Machlup action functional for stochastic partial differential equations with Levy noise
Jianyu Hu, Jinqiao Duan
This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian m…
Linear Response Theory for Nonlinear Stochastic Differential Equations with -stable Lévy Noises
Qi Zhang, Jinqiao Duan
We consider a nonlinear stochastic differential equation driven by an -stable Lévy process (). We first obtain some regularity results for the probability density of its…
Analysis of multiscale methods for stochastic dynamical systems driven by -stable processes
Yanjie Zhang, Xiao Wang, Zibo Wang +1
In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by -stable processes, which…
An averaging principle for fractional stochastic differential equations with Lévy noise
Wenjing Xu, Jinqiao Duan, Wei Xu
This paper is devoted to the study of an averaging principle for fractional stochastic differential equations in Rnwith Lévy motion, using an integral transform method. We obtain a…
Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise
Yubin Lu, Jinqiao Duan
It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the inv…
The persistence of synchronization under -stable noise
Yanjie Zhang, Li Lin, Jinqiao Duan +1
This work is about the synchronization of nonlinear coupled dynamical systems driven by -stable noise. Firstly, we provide a novel technique to construct the relationship betwee…
Rolling with Random Slipping and Twisting: A Large Deviation Point of View
Qiao Huang, Wei Wei, Jinqiao Duan
We study a rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against Euclidean space, where the rolling is coupled with r…
Large Deviations for Stochastic Differential Equations Driven by Semimartingales
Qiao Huang, Wei Wei, Jinqiao Duan
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of dr…
Effective Approximation for a Nonlocal Stochastic Schrödinger Equation with Oscillating Potential
Li Lin, Meihua Yang, Jinqiao Duan
We study the effective approximation for a nonlocal stochastic Schrodinger equation with a rapidly oscillating, periodically time-dependent potential. We use the natural diffusive…
Homogenization of Non-symmetric Jump Processes
Qiao Huang, Jinqiao Duan, Renming Song
We study the homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non…
Effective filtering analysis for non-Gaussian dynamic systems
Yanjie Zhang, Huijie Qiao, Jinqiao Duan
This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynami…
Effective reduction for a nonlocal Zakai stochastic partial differential equation in data assimilation
Li Lin, Meihua Yang, Jinqiao Duan
We study the effective reduction for a nonlocal stochastic partial differential equation with oscillating coefficients. The nonlocal operator in this stochastic partial differentia…
Effective Filtering on a Random Slow Manifold
Huijie Qiao, Yanjie Zhang, Jinqiao Duan
This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Sec…
Schauder estimates for stochastic transport-diffusion equations with Lévy processes
Jinlong Wei, Jinqiao Duan, Guangying Lv
We consider a transport-diffusion equation with Lévy noises and Hölder continuous coefficients. By using the heat kernel estimates, we derive the Schauder estimates for the mild so…
Martingale and Weak Solutions for a Stochastic Nonlocal Burgers Equation on Bounded Intervals
Guangying Lv, Jinqiao Duan
This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution…
Topological equivalence for discontinuous random dynamical systems and applications
Huijie Qiao, Jinqiao Duan
After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differ…
Stationary Measures for Stochastic Differential Equations with Jumps
Huijie Qiao, Jinqiao Duan
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through…
Ensemble Averaging for Dynamical Systems under Fast Oscillating Random Boundary Conditions
Wei Wang, Jian Ren, Jinqiao Duan +1
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principl…
Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems
Hongbo Fu, Xianming Liu, Jinqiao Duan
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of f…