13 papers · 1 filter
Hydrodynamic and Stochastic Limits of Space-Time Hawkes Processes
Fuqing Gao, Yingli Wang, Lingjiong Zhu
We study the large-scale behavior of critical and nearly critical space-time Hawkes processes initialized by a prescribed Poisson field of past events. The density of this initial…
Stability and Diversity of Networked Self-Consuming Generative Ecosystems
Xiukun Wei, Yang Zhang, Xueru Zhang
The widespread deployment of generative AI has made it increasingly difficult to distinguish synthetic content from real data. Consequently, synthetic data is inevitably incorporat…
Fully Deterministic Shallow Neural Networks with Localized Activations. Part II: Condition Number Estimates
Ran Bi, Weibing Deng
We prove positive definiteness and quantitative condition-number bounds for continuous Sobolev Gram matrices of deterministic shallow networks with Gaussian and tanh-difference act…
Moderate Deviations for Nonlinear Hawkes Processes
Yingli Wang, Lingjiong Zhu
A Hawkes process is a simple point process whose intensity depends on its history; the resulting dynamics are generally non-Markovian. We establish a sample-path moderate deviation…
Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling
Wujun Lv, Xiaoyu Wang, Yingli Wang +1
Hessian-free high-resolution (HFHR) dynamics augments underdamped Langevin dynamics (ULD) with reversible position diffusion for sampling problems that arise in machine learning. W…
Sharp hypocoercive convergence estimates for underdamped Langevin dynamics with specular reflection
Hengrong Du, Qi Feng, Lingjiong Zhu
We study the underdamped (kinetic) Langevin dynamics confined to a bounded domain by specular reflection of the velocity at the boundary. This process is the…
Microstructural Foundation for the Rough Hawkes--Heston Model
Yingli Wang, Yinhao Wu, Lingjiong Zhu
Hawkes-based microstructural foundations for rough volatility, leverage, and rough Heston-type limits were developed by El Euch et al. (2018, Finance Stoch., 22(2), 241--280) and c…
An Eyring--Kramers Law for the Hypoelliptic Third-Order Langevin Diffusion
Yingli Wang, Lingjiong Zhu
We prove an Eyring--Kramers law for metastable transitions of the hypoelliptic third-order Langevin diffusion in the low-temperature limit. This diffusion is a three-level Markovia…
Weak Equilibrium Measures and Capacity--Hitting Identities for the Hypoelliptic Third-Order Langevin Diffusion
Ping He, Xiaodan Li, Yingli Wang +1
We construct weak equilibrium measures and weak capacities for the hypoelliptic third-order Langevin diffusion motivated by an accelerated sampling algorithm (Mou et al. (2021) \te…
Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithms
Bingye Ni, Xiaoyu Wang, Yingli Wang +1
We study the leading-order fluctuation of stochastic gradient Euler-Maruyama estimators for generalized non-reversible Langevin dynamics. Under structural assumptions tailored to t…
VIX options in Bergomi models
Desen Guo, Dan Pirjol, Lingjiong Zhu
We present a study of the leading-order asymptotics for VIX option prices in Bergomi models in the short-maturity and small volatility-of-volatility regimes. Both out-of-the-money…
VIX and European options with jumps in the short-maturity regime
Desen Guo, Dan Pirjol, Xiaoyu Wang +1
We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OT…
Sampling non-log-concave densities via Hessian-free high-resolution dynamics
Xiaoyu Wang, Yingli Wang, Lingjiong Zhu
We study the problem of sampling from a target distribution on , where can be non-convex, via the Hessian-free high-resolution (HFHR) dyna…