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Yingli Wang

Publications and source records attributed to Yingli Wang.

At least 19 recordsLinked to original sources
arXiv2026

Fluctuations, Moderate and Large Deviations about Hydrodynamic Limits of Space-Time Hawkes Processes

We study Gaussian fluctuations, moderate and large deviations around the high-density hydrodynamic limit of critical and nearly critical space-time Hawkes processes initialized by a prescribed Poisson field of past events, with no subsequent immigration. Under a finite mean reproduction delay and centered displacements with finite spatial covariance, a positive cluster-transform estimate yields a distribution-valued central limit theorem (CLT) and a moderate deviation principle (MDP) throughout the moderate range. For finite nonzero mass of the initial profile, we obtain a full large deviation principle (LDP) for the space-time event measure in the vague topology; its good rate function is a quadratic branching-control energy with a prescribed initial trace and a finite-mass domain. The lower bound uses an explicit approximation by smooth reproduction controls, and the upper bound uses a microscopic exponential martingale and a global generator approximation. We distinguish exact-mean centering from PDE centering and compute deterministic bias corrections under second delay and fourth spatial moments. For a factorized heavy-tail power-law delay, we establish the CLT, MDP, and full measure-valued LDP for the space-time measure, with finite nonzero mass of the initial profile for the LDP. Its fractional control energy retains the source generated by the prescribed past. A source-preserving regularization proves approximation of every finite-action measure. Compact-kernel bounds for initial profiles of infinite mass and the degenerate case of a zero initial profile are stated separately.

math.PR↗
arXiv2026

Hydrodynamic and Stochastic Limits of Space-Time Hawkes Processes

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 field separates three macroscopic regimes. In the high-density regime, fluctuations average out and the event measure converges to a hydrodynamic limit which is a deterministic diffusion profile. At the fluctuation threshold, random branching remains visible and produces a measure-valued stochastic limit. Below the threshold, the rescaled event measure vanishes locally even though its mean generally remains nontrivial, with rare large clusters accounting for the surviving mean. For reproduction delays with finite mean, the critical limits are described by heat flow and the occupation measure of a branching diffusion. A nearly critical perturbation introduces linear decay without changing the three-regime structure. Heavy-tailed delays lead to a different balance between time and space: the mean follows a fractional diffusion law, the stochastic limit is a superprocess occupation measure on time-space, characterized by a nonlinear fractional equation, and the past persists as a temporal memory term. We also determine how the scaling of the Poisson past must be matched to the observation scales and show that, in one spatial dimension, a shorter observation window recovers stochastic behavior hidden in the sparse regime. The results allow bounded initial profiles with possibly infinite total mass and describe the limits directly at the level of locally finite event measures.

math.PR↗
arXiv2026

Accelerating Non-Smooth and Heavy-Tailed Sampling

Anchored Langevin dynamics (ALD) is useful for non-smooth sampling where the density of the target distribution is possibly non-differentiable and heavy-tailed; reflected anchored Langevin dynamics (RALD) can sample possibly non-differentiable target density on a constrained domain. In this paper, we propose and study non-reversible anchored Langevin dynamics (NALD) for sampling possibly non-differentiable and heavy-tailed target density in the Euclidean space and the non-reversible reflected anchored Langevin dynamics (NRALD) for sampling possibly non-differentiable target density in the constrained space. Our construction adds a circulation drift generated by a possibly state-dependent divergence-free skew-symmetric matrix field and a stream potential. It preserves the target distribution without requiring derivatives of target density, admits a random-time-change representation, and applies both on the whole Euclidean space and on bounded domains with normal reflection. By breaking reversibility, we show that NALD and NRALD can converge to their target distributions faster than their reversible counterparts via finite-time non-asymptotic convergence analysis, a large deviations analysis and asymptotic variance reduction. Numerical experiments demonstrate the efficiency of the proposed algorithms.

stat.ML↗
arXiv2026

Reflected Anchored Langevin Algorithms

First order Langevin algorithms for constrained sampling in machine learning, such as projected Langevin Monte Carlo which are based on discretizations of reflected Langevin dynamics, require differentiable log densities that limits their applicability. This paper introduces reflected anchored Langevin dynamics (RALD), a reflected diffusion that converges to non-differentiable targets on constrained domains. The method uses a smooth anchored reference potential and multiplies the drift and noise covariance of its reflected Langevin dynamics by the same state dependent scaling factor. Its Euler-Maruyama discretization with projection gives reflected anchored Langevin Monte Carlo (RALMC) algorithm. We prove explicit convergence bounds and iteration complexity for RALMC in the 2-Wasserstein distance to the target distribution. Numerical experiments are provided to illustrate the theoretical predictions and the empirical performance of the method.

stat.ML↗
arXiv2026

A Hawkes Microfoundation for Multitype Inverse Gaussian Subordinators

We provide an event-level Hawkes microfoundation for a multitype inverse-Gaussian stochastic clock. We show that the event counts and integrated intensities of nearly critical multivariate linear Hawkes processes converge jointly to a multivariate pure-jump subordinator when reproduction delays have finite mean and immigration is balanced so that rare large families remain visible. The dependence among the limiting coordinates is inherited from microscopic cross-excitation, and the limit admits a Brownian additive-field first-passage representation. We call this process the multitype inverse-Gaussian subordinator. Its diagonal case consists of independent classical inverse-Gaussian subordinators, with the univariate model as a further special case. The square-root specialization recovers the inverse-Gaussian clock obtained at the boundary of hyper-rough square-root models by Abi Jaber--Attal--Rosenbaum (\textit{Ann. Appl. Probab.} \textbf{36}(4): 3635--3660, 2026). Our cluster proof exposes the underlying mechanism: finite-variance near-critical branching creates rare but macroscopic families, while their internal timing disappears on the observation scale, so each family becomes a jump. We also clarify the relation with the multivariate Hawkes scaling theory of Xu (arXiv:2412.14459): its diagonal-atom condition yields the diagonal specialization, whereas the genuinely coupled limit requires a separate uniqueness argument. In addition, under a common tilted-stability condition, we replace the high-intensity assumption in that theory by a weaker accumulated-activity condition and provide the Riccati identification needed when the potential has an atom. We strengthen convergence of the count and compensator and extend the scalar conclusion to finite-variance age-dependent branching clusters.

math.PR↗
arXiv2026

Global Convergence of Third-Order Langevin Dynamics for Non-Convex Optimization via Simulated Annealing

We study global convergence guarantees of third-order Langevin dynamics for non-convex optimization via simulated annealing with fixed friction and decreasing noise. An explicit three-block distorted entropy transfers dissipation from the noisy auxiliary variable to the full state. Under dissipativity, regularity, and low-temperature functional-inequality assumptions, logarithmic cooling drives the objective values to the global minimum in probability at the barrier-controlled kinetic rate. For the exact-force-integral and midpoint three-stage discretizations, polynomially decreasing steps preserve this rate on the physical time scale. The cubic local endpoint estimate gives a less restrictive sufficient step-size condition than the available frozen-force kinetic result. A comparison with the one-gradient UBU integrator shows how its centered stochastic local error leads, under the same strong-coupling analysis, to a smaller sufficient iteration exponent. Numerical experiments are conducted to illustrate our theory. For a double well objective, third-order Langevin terminal-success point estimates are higher than UBU at both a common horizon and an equal gradient budget. For a high-dimensional nonconvex neural-network objective using synthetic data, independently tuned UBU and third-order Langevin schemes both outperform overdamped Langevin dynamics; the third-order Langevin point estimate is higher. For the same neural-network objective on real data, we show the same point-estimate ordering for best-basin probability and post-quench test accuracy. Numerical code and associated experiment results are publicly available at https://github.com/gagawjbytw/simulated-annealing-third-order-langevin.

math.NA↗
arXiv2026

Moderate Deviations for Nonlinear Hawkes Processes

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 principle for a nonlinear Hawkes process in the full moderate regime. Since a Poisson cluster representation is unavailable for nonlinear Hawkes processes, we use the past configuration as a Markov state and construct a potential, or Poisson corrector, for the centered stochastic intensity. A monotone Poisson coupling shows that the add-one increment of the corrector is uniformly bounded. The centered counting process is consequently the sum of a martingale with bounded jumps and an exponentially negligible boundary term. Exponential stabilization of the predictable quadratic variation follows from the process-level large deviation principle for nonlinear Hawkes processes. The martingale moderate deviation theorem then yields the result for every scale between the central-limit and large-deviation scales. The same construction gives a response formula for the asymptotic variance and, in particular, verifies that the variance dominates the stationary mean intensity in the self-exciting case.

math.PR↗
arXiv2026

Variance-Optimal Hedging in the Rough Hawkes--Heston Model

We study variance-optimal stock hedging and the convergence of approximate strategies in the rough Hawkes--Heston model. Starting from the model's affine conditional transform and the affine Volterra jump framework, we obtain semi-explicit hedges for European calls and a representation of the minimum quadratic error through the Galtchouk--Kunita--Watanabe projection. Our main approximation result keeps the original stock, variance driver, and information flow fixed while regularizing the kernel used to evaluate the hedge. To handle singular memory and common marked jumps, we construct the approximate holdings from histories available before trading and preserve the conditional transform's random modulus envelope. Riccati--Volterra stability and weighted truncation then yield convergence in the original stock's trading norm on compact Fourier intervals. For calls, a joint choice of kernel regularization and Fourier cutoff gives convergence of the initial capitals and strategies, uniform-in-time square-mean convergence of continuous-time gains, and convergence of the terminal mean-square error to the variance-optimal value. A numerical experiment with shifted fractional kernels illustrates the construction on common original-market paths.

q-fin.MF↗
arXiv2026

Trustworthy Second-hand Marketplace for Built Environment

The construction industry faces significant challenges regarding material waste and sustainable practices, necessitating innovative solutions that integrate automation, traceability, and decentralised decision-making to enable efficient material reuse. This paper presents a blockchain-enabled digital marketplace for sustainable construction material reuse, ensuring transparency and traceability using InterPlanetary File System (IPFS). The proposed framework enhances trust and accountability in material exchange, addressing key challenges in industrial automation and circular supply chains. A framework has been developed to demonstrate the operational processes of the marketplace, illustrating its practical application and effectiveness. Our contributions show how the marketplace can facilitate the efficient and trustworthy exchange of reusable materials, representing a substantial step towards more sustainable construction practices.

cs.DC↗
arXiv2026

Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling

Hessian-free high-resolution (HFHR) dynamics augments underdamped Langevin dynamics (ULD) with reversible position diffusion for sampling problems that arise in machine learning. We establish an explicit quantitative contraction rate for HFHR dynamics under a position Poincaré inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, where the potential function is not necessarily convex. An adapted time-augmented Poincaré inequality yields an explicit rate that improves upon the contraction rate of the underdamped Langevin dynamics. We also give a weak-solution construction and a self-contained spectral proof of the divergence lemma underlying the argument. For HFHR Monte Carlo (HFHRMC) algorithm, which is based on a discretization scheme of HFHR dynamics, we use a path-space Girsanov argument to obtain a non-asymptotic convergence bound and an explicit iteration complexity in total variation distance. The bounds hold for every $α\geq0$ and $γ>0$ and remain regular at the ULD endpoint. Optimizing the iteration complexity bound yields a positive, accuracy-dependent position-diffusion parameter at finite accuracy, while its leading high-accuracy order coincides with that of the optimized ULD endpoint. Our iteration complexity bound improves upon the existing work on HFHR algorithms. Numerical experiments including Bayesian learning problems on real data are provided to illustrate the effect of positive $α$ and its benefit.

stat.ML↗
arXiv2026

An Eyring--Kramers Law for the Hypoelliptic Third-Order Langevin Diffusion

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 Markovian lifting of Langevin dynamics: the Brownian noise acts only on the highest auxiliary variable and reaches the position variable through a third-order H"ormander chain. For a double-well potential with a unique index-one transition saddle, we determine both the Arrhenius exponential scale and the sharp prefactor of the mean transition time. The prefactor is governed by the unique positive unstable rate of the deterministic linearization at the saddle, equivalently the positive root of a cubic polynomial. Our proof combines a weak-capacity framework with a saddle-adapted boundary layer, an explicit Gaussian current calculation, committor localization, and intrawell flatness. Under matched kinetic normalizations, the resulting metastable prefactor is strictly smaller than its underdamped counterpart. A numerical experiment for a one-dimensional double well illustrates the Arrhenius scaling and the predicted prefactor comparison.

math.PR↗
arXiv2026

Microstructural Foundation for the Rough Hawkes--Heston Model

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 connected to the affine rough Heston framework of El Euch and Rosenbaum (2019, Math. Finance, 29(1), 3--38). The rough Hawkes--Heston model with common price--volatility jumps of Bondi et al. (2024, Math. Finance, 34(4), 1197--1241) extends this framework by adding state-dependent common jumps to rough affine volatility. We provide a microstructural foundation for its variance and common-jump mechanism by constructing a Poisson-embedded marked Hawkes order-flow model. Ordinary arrivals generate rough continuous volatility and leverage through a nearly unstable heavy-tailed Hawkes mechanism, while rare marked arrivals represent common shock events that produce simultaneous price jumps and volatility excitation. Under the nearly unstable scaling and the reduced-form admissibility conditions, the complete rescaled price/variance/jump system converges along the full sequence to the unique complete canonical rough Hawkes--Heston weak solution. The Hawkes renewal structure yields a Mittag--Leffler Volterra representation, which is then rewritten in Riemann--Liouville fractional form. The limiting coefficients are expressed explicitly in terms of the microscopic parameters. The construction provides a microstructural foundation for the variance and common-jump mechanism of the rough Hawkes--Heston model. Numerical experiments illustrate the convergence of our microstructural foundation to the rough Hawkes-Heston model.

q-fin.MF↗
arXiv2026

Weak Equilibrium Measures and Capacity--Hitting Identities for the Hypoelliptic Third-Order Langevin Diffusion

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) \textit{J. Mach. Learn. Res.}, \textbf{22}(42), 1--41). In this process, the Brownian noise acts only in the highest-order auxiliary variable and reaches the physical variables through a step-three Hörmander chain, so the standard uniformly elliptic boundary-flux theory is not directly applicable at characteristic points of phase-space balls. We prove an elliptic-regularization stability theorem for the corresponding hitting laws and then define the weak equilibrium measure and weak capacity. The proof combines the boundary-hitting stability strategy of Lee--Ramil--Seo (2026, \textit{arXiv:2503.12610v2}) with localized hypoelliptic heat-kernel estimates (Pigato (2022) \textit{Stoch. Process. Appl.}, \textbf{145}, 117--142) adapted to the third-order chain. We obtain the bounded-domain weak capacity--hitting identity and a Lyapunov drift argument in the spirit of Lee--Ramil--Seo that yields positive Harris recurrence and extends the construction to a whole-space weak equilibrium measure, and whole-space capacity--hitting identity.

math.PR↗
arXiv2026

Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithms

We study the leading-order fluctuation of stochastic gradient Euler-Maruyama estimators for generalized non-reversible Langevin dynamics. Under structural assumptions tailored to the small-stepsize central limit theorem and under an unbiased stochastic gradient oracle, we prove that the empirical average over a horizon of order the inverse squared stepsize satisfies a central limit theorem in the vanishing-stepsize regime. The limiting variance is characterized through the Poisson equation of the limiting full-gradient diffusion. We then rewrite this constant in an operator form that links it to the continuous-time asymptotic variance and, under standard operator-theoretic assumptions, derive a sufficient condition under which an anti-symmetric perturbation strictly reduces the leading-order fluctuation constant relative to the reversible baseline. We also identify bounded smooth predictive observables that re directly covered by the main theorem. As a separate Gaussian calculation beyond the bounded-test-function regime, we obtain closed-form formulas for quadratic Hamiltonians and linear observables. The framework covers non-reversible Langevin dynamics and augmented-state examples including Hessian-free high-resolution dynamics and a positive-definite subclass of gradient-adjusted underdamped Langevin dynamics that allow stochastic gradients. Numerical experiments on basic examples and Bayesian linear regression using synthetic data, and Bayesian logistic regression using real data support the predicted Gaussian fluctuations and show that the non-reversible schemes consistently reduce the root mean squared error (RMSE) relative to their reversible baselines.

stat.ML↗
arXiv2026

Rough Heston model as the scaling limit of bivariate cumulative heavy-tailed INAR processes: Weak-error bounds and option pricing

We study nearly unstable bivariate cumulative heavy-tailed INAR($\infty$) processes and show that, under a one-factor parameterization and a suitable scaling, they converge to the rough Heston model. This yields a discrete-time microstructural route to the joint price-variance dynamics and gives explicit formulas linking the INAR asymmetry parameters to the leverage correlation and diffusion scale of the limiting volatility process. On the pricing side, we derive the exact finite-$τ$ transform recursion and reduce it, in the diffusive scaling regime, to a quadratic discrete Volterra equation. We then compare this discrete equation with the continuous fractional Riccati equation from the rough Heston model. Under an admissible-strip assumption and local-in-frequency bounds, we obtain weak-error estimates for the truncated Carr--Madan pricing functional on bounded frequency windows of the form $C_1τ^{-α}+C_2(α)τ^{-(1-α)}$, where the second branch comes from the discrete-to-continuous Volterra comparison. The coefficient $C_2(α)$ collects the vanishing contributions arising from both the weakly singular baseline quadrature and the discrete-to-continuous resolvent comparison, and satisfies $C_2(α)\to0$ as $α\uparrow1^-$. We also develop an FFT-accelerated CDQ simulator with $\mathcal O(τ\log^2τ)$ complexity per path and use it to price European and path-dependent options, examine the classical limit $α=1$, and illustrate implied-volatility diagnostics.

math.PR↗
arXiv2026

Accelerating Constrained Sampling: A Large Deviations Approach

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC), based on the discretization of reflected Langevin dynamics (RLD) and more generally skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), based on the discretization of skew-reflected non-reversible Langevin dynamics (SRNLD), have been proposed and studied in the literature. This work focuses on the long-time behavior of SRNLD, where a skew-symmetric matrix is added to RLD. Although acceleration for SRNLD has been studied, it is not clear how one should design the skew-symmetric matrix in the dynamics to achieve good performance in practice. We establish a large deviation principle (LDP) for the empirical measure of SRNLD when the skew-symmetric matrix is chosen such that its product with the outward unit normal vector field on the boundary is zero. By explicitly characterizing the rate functions, we show that this choice of the skew-symmetric matrix accelerates the convergence to the target distribution compared to RLD and reduces the asymptotic variance. Numerical experiments for SRNLMC based on the proposed skew-symmetric matrix show superior performance, which validate the theoretical findings from the large deviations theory.

stat.ML↗
arXiv2026

Scaling limit of heavy tailed nearly unstable cumulative INAR($\infty$) processes and rough fractional diffusions

In this paper, we investigate the scaling limit of heavy-tailed nearly unstable cumulative INAR($\infty$) processes. These processes exhibit a power-law tail of the form $n^{-(1+α)}$ for $α\in (\frac{1}{2}, 1)$, and the $\ell^1$ norm of the kernel vector converges to 1. We demonstrate that the discrete-time scaling limit retains a long-memory property and can be viewed as an integrated fractional Cox-Ingersoll-Ross process. Moreover, we present an efficient method for simulating the fractional Cox-Ingersoll-Ross process. The simulation and Goodness-of-Fit Test code are available at https://github.com/gagawjbytw/INAR-rough-Heston.

math.PR↗