15 citations · 22 across the 14 of their papers we have counts for
15 papers
Invariant connections in geometric mechanics: reduction, nonlocality, and curvature effects
Qiao Huang
We present a systematic study on the role of invariant connections in geometric mechanics. We first develop a comprehensive theory of reduction under left- and right-invariant conn…
Geometric Methods for Stochastic Dynamical Systems: A Concise Introduction
Jinqiao Duan, Ting Gao, Qiao Huang +1
There is growing interest in stochastic dynamics in the applied mathematics, interdis-ciplinary science, and artificial intelligence communities. This book is written primarilyfor…
The stochastic Hamilton-Jacobi-Bellman equation on Jacobi structures
Pingyuan Wei, Qiao Huang, Jinqiao Duan
Jacobi structures are known to generalize Poisson structures, encompassing symplectic, cosymplectic, and Lie-Poisson manifolds. Notably, other intriguing geometric structures -- su…
Stochastic Geometric Mechanics in Nonequilibrium Thermodynamics: Schrödinger meets Onsager
Qiao Huang, Jean-Claude Zambrini
We are describing relations between Schrödinger's variational problem and Onsager's approach to nonequilibrium statistical mechanics. Although the second work on reciprocal relatio…
From Second-Order Differential Geometry to Stochastic Geometric Mechanics
Qiao Huang, Jean-Claude Zambrini
Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as…
The Most Probable Transition Paths of Stochastic Dynamical Systems: A Sufficient and Necessary Characterization
Yuanfei Huang, Qiao Huang, Jinqiao Duan
The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not s…
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…
On the Stochastic Singular Cucker--Smale Model: Well-Posedness, Collision-Avoidance and Flocking
Qiao Huang, Xiongtao Zhang
We study the Cucker--Smale (C-S) flocking systems involving both singularity and noise. We first show the local strong well-posedness for the stochastic singular C-S systems before…
Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes
Yanjie Zhang, Qiao Huang, Xiao Wang +2
We study the averaging principle for a family of multiscale stochastic dynamical systems. The fast and slow components of the systems are driven by two independent stable Lévy nois…
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…
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…
Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative -stable noises
Yanjie Zhang, Xiao Wang, Qiao Huang +2
The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric -stable noises may not adequately describe the time evolution for the probability densitie…
Homogenization of Nonlocal Partial Differential Equations Related to Stochastic Differential Equations with Lévy Noise
Qiao Huang, Jinqiao Duan, Renming Song
We study the "periodic homogenization" for a class of nonlocal partial differential equations of parabolic-type with rapidly oscillating coefficients, related to stochastic differe…
Maximum principles for nonlocal parabolic Waldenfels operators
Qiao Huang, Jinqiao Duan, Jiang-Lun Wu
As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructi…