11 papers
RELTA-SGLD: Relative-Growth Localized Taming for Nonconvex Stochastic-Gradient Langevin Learning
Yiwei Zhou, Ziheng Chen
We introduce RELTA-SGLD, a taming scheme that stabilizes superlinear stochastic-gradient updates while reducing unnecessary suppression of the original learning drift. A threshold…
Strong order one-half convergence of a coupled tamed Euler--Peano scheme for reflected stochastic differential equations with super-linearly growing coefficients
Ziheng Chen, Caiyun Hua, Meng Cai
We study strong numerical approximations for reflected stochastic differential equations in possibly unbounded convex domains with super-linearly growing drift and diffusion coeffi…
Deterministic Envelopes for Tamed SGLD: Decoupling Stochastic Gradient Noise and Localizing Taming
Yiwei Zhou, Ziheng Chen
Stochastic gradient Langevin algorithms often use tamed denominators to stabilize superlinear drifts. This paper shows that when the denominator depends on the current stochastic g…
Weak order one convergence of structure-preserving stochastic theta methods for stochastic differential algebraic equations with time-dependent singular matrices
Caiyuan Zhu, Ziheng Chen, Lin Chen +1
This paper studies the weak convergence order of structure-preserving stochastic theta methods for a class of index- stochastic differential algebraic equations with time-depend…
Stress Amplified Resilience: ESG and Joint Fragility in Equity Markets
Minxuan Hu, Jiayu Yi, Ziheng Chen +2
Market stress rarely harms investors through one channel alone. Losses, volatility spikes, and deteriorating tradability often arrive together. We examine whether ESG is associated…
Weak convergence order of stochastic theta method for SDEs driven by time-changed Lévy noise
Ziheng Chen, Jiao Liu, Meng Cai
This paper studies the weak convergence order of the stochastic theta method for stochastic differential equations (SDEs) driven by time-changed Lévy noise under global Lipschitz a…
The continuity of Beurling density and Beurling dimension of spectra of a class of self-affine spectral measures
Zi-Yun Chen, Zhi-Yi Wu, Min-Min Zhang
It is well-known that the Beurling dimension of the spectra of certain singularly continuous spectral measures possesses an intermediate property. In this paper, we establish that…
A Dilation-based Seamless Multiscale Method For Elliptic Problems
Ziheng Chen, Björn Engquist
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency.…
Strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise
Ziheng Chen, Jiao Liu, Anxin Wu
This work investigates the strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise under the globally Lipschitz conditions. Based on the…
Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions
Jingjing Cai, Ziheng Chen, Yuanling Niu
This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect…
Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions
Ziheng Chen, Liangmin Cao, Lin Chen
This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the ex…