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Yingli Wang

Publications and source records attributed to Yingli Wang.

At least 19 recordsLinked to original sources
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

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 Poincar\'e inequality, weighted Hessian and Laplacian bounds, and a compact Sobolev embedding, where the potential function is not necessarily convex. An adapted time-augmented Poincar\'e 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 $\alpha\geq0$ and $\gamma>0$ 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 $\alpha$ and its benefit.

stat.ML↗
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

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

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 H\"ormander 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

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↗
arXiv2026

Sampling non-log-concave densities via Hessian-free high-resolution dynamics

We study the problem of sampling from a target distribution $π(q)\propto e^{-U(q)}$ on $\mathbb{R}^d$, where $U$ can be non-convex, via the Hessian-free high-resolution (HFHR) dynamics, which is a second-order Langevin-type process that has $e^{-U(q)-\frac12|p|^2}$ as its unique invariant distribution, and it reduces to kinetic Langevin dynamics (KLD) as the resolution parameter $α\to0$. The existing theory for HFHR dynamics in the literature is restricted to strongly-convex $U$, although numerical experiments are promising for non-convex settings as well. We focus on studying the convergence of HFHR dynamics when $U$ can be non-convex, which bridges a gap between theory and practice. Under a standard assumption of dissipativity and smoothness on $U$, we adopt the reflection/synchronous coupling method. This yields a Lyapunov-weighted Wasserstein distance in which the HFHR semigroup is exponentially contractive for all sufficiently small $α>0$ whenever KLD is. We further show that, under an additional assumption that asymptotically $\nabla U$ has linear growth at infinity, the contraction rate for HFHR dynamics is strictly better than that of KLD, with an explicit gain. As a case study, we verify the assumptions and the resulting acceleration for three examples: a multi-well potential, Bayesian linear regression with $L^p$ regularizer and Bayesian binary classification. We conduct numerical experiments based on these examples, as well as an additional example of Bayesian logistic regression with real data processed by the neural networks, which illustrates the efficiency of the algorithms based on HFHR dynamics and verifies the acceleration and superior performance compared to KLD.

math.PR↗
arXiv2025

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↗
arXiv2025

Regime-Switching Langevin Monte Carlo Algorithms

Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic differential equations in the probability literature, we propose and study regime-switching Langevin dynamics (RS-LD) and regime-switching kinetic Langevin dynamics (RS-KLD). Based on their discretizations, we introduce regime-switching Langevin Monte Carlo (RS-LMC) and regime-switching kinetic Langevin Monte Carlo (RS-KLMC) algorithms, which can also be viewed as LMC and KLMC algorithms with random stepsizes. We also propose frictional-regime-switching kinetic Langevin dynamics (FRS-KLD) and its associated algorithm frictional-regime-switching kinetic Langevin Monte Carlo (FRS-KLMC), which can also be viewed as the KLMC algorithm with random frictional coefficients. We provide their 2-Wasserstein non-asymptotic convergence guarantees to the target distribution, and analyze the iteration complexities. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of our proposed algorithms.

stat.CO↗
arXiv2025

Statistical Inference for Cumulative INAR($\infty$) Processes via Least-Squares

This paper investigates the cumulative Integer-Valued Autoregressive model of infinite order, denoted as INAR($\infty$), a class of processes crucial for modeling count time series and equivalent to discrete-time Hawkes processes. We propose a computationally efficient conditional least-squares (CLS) estimator to address the challenge of parameter inference in this infinite-dimensional setting. We establish the key theoretical properties of the estimator, including its consistency and asymptotic normality. A central contribution is the rigorous treatment of its large-sample distribution in a framework where the parameter dimension grows with the sample size, for which we derive the corresponding sandwich-form covariance matrix. The theoretical results are substantiated through comprehensive Monte Carlo simulations. These experiments demonstrate that the estimator's accuracy and stability systematically improve as the sample size increases, confirming its consistency. Furthermore, we show that the estimator's finite-sample distribution is well-approximated by a normal distribution, and this approximation becomes more robust with larger samples. Our work provides a complete and practical framework for statistical inference in cumulative INAR($\infty$) models. The code to reproduce the numerical experiments is publicly available at https://github.com/gagawjbytw/INAR_estimation.

math.ST↗
arXiv2025

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↗
arXiv2022

Limit theorems for Hull-White model with Hawkes jumps

In the present paper, we obtain limit theorems for a catogary of Hull-White models with Hawkes jumps including law of large numbers, central limit theorem, and large deviations. In the field of interest rate modeling, it is meaningful in characterizing a long-term rate of return.

math.PR↗
arXiv2020

Evolution of the Chinese Guarantee Network under Financial Crisis and Stimulus Program

Our knowledge about the evolution of guarantee network in downturn period is limited due to the lack of comprehensive data of the whole credit system. Here we analyze the dynamic Chinese guarantee network constructed from a comprehensive bank loan dataset that accounts for nearly 80% total loans in China, during 01/2007-03/2012. The results show that, first, during the 2007-2008 global financial crisis, the guarantee network became smaller, less connected and more stable because of many bankruptcies; second, the stimulus program encouraged mutual guarantee behaviors, resulting in highly reciprocal and fragile network structure; third, the following monetary policy adjustment enhanced the resilience of the guarantee network by reducing mutual guarantees. Interestingly, our work reveals that the financial crisis made the network more resilient, and conversely, the government bailout degenerated network resilience. These counterintuitive findings can provide new insight into the resilience of real-world credit system under external shocks or rescues.

q-fin.RM↗
arXiv2019

Network Subgraphs of the heterogeneous Chinese credit system

In this study, we investigate the evolution of Chinese guarantee networks from the angle of sub-patterns. First, we find that the mutual, 2-out-stars and triangle sub-patterns are motifs in 2- and 3-node subgraphs. Considering the heterogeneous financial characteristics of nodes, we find that small firms tend to form a mutual guarantee relationship and large firms are likely to be the guarantors in 2-out-stars sub-patterns.

cs.CE↗