Hawkes Processes

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14 papers4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Oct 14, 2026

Projected Wasserstein-Fisher-Rao Flows for Hawkes Background-Intensity Estimation

We consider the problem of estimating the background intensity of a Hawkes process when the triggering mechanism is known, treating the background as an unknown finite positive measure with a regular density. We propose a likelihood-based variational approach based on the Wasserstein-Fisher-Rao geometry. In this setting, the relevant first variations are naturally distribution-valued and therefore fall outside the classical gradient-flow formulation. We develop a distributional framework for the resulting dynamics and give them a finite-dimensional meaning through projections onto statistical manifolds. We identify the true background as the unique zero of a limiting generalized gradient and, under suitable stability, compactness, integrability and approximation conditions, establish a conditional consistency theorem for measurable estimators satisfying the empirical projected equations on events whose probabilities tend to one. Finally, we specialize the construction to Gaussian-mixture manifolds and obtain an explicit finite-dimensional scheme.

Isaias Banales, Arturo Jaramillo

Facultad de Ciencias, Universidad Aut´onoma de M´exico · Department of Probability and Statistics, Centro de Investigaci´on en Matem´aticas A.C., Guanajuato, M´exico

Hawkes ProcessesTemporal Point ProcessesWasserstein Gradient Flows
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Oct 12, 2026

Reinforcement Learning with Hawkes-Structured Networks for Market Making

Market making under realistic order-flow dynamics is challenging due to the clustered, self-exciting nature of order arrivals, which are naturally modeled by non-Markovian Hawkes processes. We propose a model-free reinforcement learning (RL) framework for market making with general Hawkes order-flow dynamics. We first establish non-asymptotic performance bounds that quantify the loss incurred by approximating the infinite-dimensional Hawkes state using a finite collection of exponentially weighted features. Guided by this analysis, we introduce the Hawkes-Structured Network (HSN), a novel neural architecture that encodes historical order flow through a learnable mixture-of-exponentials filter. HSN is trained end-to-end using model-free RL, jointly optimizing the feature representation and quoting policy directly from reward feedback. Experiments on single- and multi-asset market-making problems with mixture-of-exponentials, power-law, and regime-switching kernels demonstrate that HSN outperforms general-purpose neural architectures, achieving higher trading rewards while implicitly recovering the underlying order-flow intensities.

Fernando Acero, Philipp Plank, Yufei Zhang

Department of Mathematics, Imperial College London, United Kingdom

Hawkes ProcessesNon-Markovian RLAlgorithmic TradingReinforcement LearningRepresentation Learning for RLModel-Free RL
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Oct 10, 2026

Exact Phase-Type Point Processes for Certified Measurement and Prediction of Event Streams

Temporal point processes are used both to measure market mechanisms, for example how fast prices absorb news and how much of the reaction is the market responding to itself, and to predict the next event. We show that one algebraic object, the phase-type (Erlang-chain) state space, serves both purposes with exact likelihoods. For measurement, we build a multiscale phase-type Hawkes process whose parameters all enter linearly. Its log-likelihood is concave, and we compute the global maximum together with a Fenchel duality-gap certificate. A Markov embedding gives the response to an exogenous shock, echoes included, in closed form, and this response is stable if and only if the spectral radius of the branching matrix is below one. Applied to six markets around 670 scheduled macroeconomic releases (2022-2026) with a built-in placebo test, the model shows that the direct reaction to CPI, payrolls, PPI and the FOMC statement is absorbed in about a second, while the market's own echoes stretch half of the response to 16-137 s. For prediction, we introduce EPT-X, a neural point process that adds a history-dependent mixture-of-Erlang renewal channel to a linear Hawkes backbone. Its intensity and compensator remain in closed form, its states follow an affine recursion that trains with a parallel scan, and it can start from the certified fit of the measurement model. EPT-X has the best test likelihood on all five LOBSTER order-book streams and on Retweet and Taobao, and is level with the best published model on StackOverflow. We also find that the EasyTPP implementation of IntensityFree clamps short inter-event times before scoring, and that the gaps of the EasyTPP Amazon data are uniform on two fixed intervals.

Sayak Dutta

Hawkes ProcessesTemporal Point ProcessesEvent Time PredictionQuantitative Finance
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Sep 25, 2026

When Should a Human Take Back Control? Optimal Delegation under Turbulent AI Risk

Deploying AI systems requires deciding when to delegate tasks and when humans should intervene to monitor and mitigate risk induced by AI operations. These decisions are challenging when failures cluster: a hallucination or harmful output can trigger further errors, creating periods of elevated risk. We introduce a continuous-time framework for learning adaptive human oversight under such turbulent AI risk. Existing oversight and delegation formulations condition on history but do not model incident clustering, or its suppression by supervision effort, jointly with the delegation decision and this study fixes this gap. The self-exciting dynamics capture how risk events increase the likelihood of subsequent events, making their timing and history central to decision-making. We formulate a stochastic control problem combining human actions, monitoring effort, and switching between human-AI-assisted operation and full AI delegation, balancing operational rewards against oversight costs, and cascading AI-failures and induced uncertainty. Human participation is an endogenous component of risk management: the policy determines both when oversight is needed and how much effort to allocate. We study a relaxed switching formulation and propose Hawkes-PPO, a policy-gradient method that uses a bank of exponential filters of observed incident times. In a synthetic environment it attains a higher risk-adjusted objective than either fixed regime and approaches an approximate full-information oracle. We illustrate our results with numerical simulations by examining how cascade risks influence intervention and delegation, connecting reinforcement learning with adaptive human oversight of AI systems. In particular, we illustrate the benefit of our switching strategy and Hawkes-PPO algorithm to monitor the project efficiently along time, reducing turbulent risks occurrences and costs.

Haoze Yan, Julien Roze, Ved Upadhyay +2

Department of Industrial Engineering and Operations Research, UC Berkeley, United States. · Stoa, United States. · Department of Cybersecurity, University at Albany, SUNY, United States.

Hawkes ProcessesHuman Oversight of AIRisk-Sensitive RL
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Sep 19, 2026

Robust Market Making with Hawkes Order Flow and Price Impact via Adversarial Reinforcement Learning

Market-making strategies in real limit order book markets face substantial model uncertainty and regime-shift risk. Existing adversarial reinforcement learning approaches improve robustness by formulating the Avellaneda--Stoikov market-making problem as a zero-sum game between a market maker and an environmental adversary. However, these approaches typically rely on Poisson order arrivals and neglect trade-induced price impact, limiting their ability to capture important high-frequency market microstructure effects such as clustered order flow, self-excitation, and post-trade price feedback. We extend adversarial reinforcement learning for market making to a more complex environment with Hawkes self-exciting order arrivals and trade-induced price impact. To mitigate the increased non-stationarity introduced by the expanded regime space, we incorporate an LSTM module that explicitly models the temporal structure of recent observations. We further characterize the equilibrium properties of the proposed framework through both game-theoretic analysis and numerical experiments, and introduce a robustness evaluation protocol focused on improvements in the left tail of the return distribution. Experimental results across a range of market regimes show that the proposed method achieves improved left-tail performance in most complex microstructure environments. In particular, the gains are pronounced in regimes with strong Hawkes excitation and low-to-moderate price impact. Bootstrap tests provide no evidence that these improvements are obtained through a stronger terminal directional inventory bias. These results suggest that combining adversarial training with temporal state representation can improve the robustness of reinforcement-learning-based market-making strategies under order-flow self-excitation, price impact, and regime uncertainty.

Hao Yang, Zhenguo Xu

North China Institute of Computer System Engineering, Beijing, China · University of Science and Technology of China, Hefei, China

Adversarial MARLHawkes ProcessesFinanceAlgorithmic TradingReinforcement LearningRobust RL
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Jul 13, 2026

NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process

In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters (μ,γ,α,β)(μ,γ,α,β) directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = 0.16340.1634), followed by the LSTM (MSE = 0.17520.1752), compared to MLE (MSE = 2.80322.8032). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.

Neha Gupta, Aditya Maheshwari

Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore 453556, India.

Temporal Point ProcessesParameter EstimationHawkes Processes
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May 21, 2026

HawkesLLM: Semantic Uncertainty Propagation in Agentic Text Simulation

Agentic text-simulation systems write in sequence, with each item becoming possible context for later steps. That makes uncertainty path-dependent: an early ambiguity can affect later outputs. This paper studies this problem with HawkesLLM, a framework that separates temporal influence modeling from text generation. We represent the cascade as a network whose nodes are text-generating agents. A multivariate Hawkes process models how these nodes activate over time and which earlier node outputs should influence later prompts. A language model then writes each new event from the compact memory selected by this temporal model. We evaluate the framework on a held-out Global Database of Events, Language, and Tone (GDELT) news-cascade case study. The diagnostics track semantic alignment with local held-out references and separate local drift from global drift. In this setting, HawkesLLM improves late-stage semantic alignment under a compact prompt-memory budget.

Zewei Deng, Tinghan Ye, Liyan Xie

Department of Industrial and Systems Engineering, University of Minnesota · H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Memory-Augmented Language Model AgentsHawkes Processes
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May 8, 2026

On Observation Time for Recovering Latent Hawkes Networks

Dynamics of interacting systems in engineering, society, and nature often evolve over latent networks that govern which entities can interact. We study the problem of inferring these networks from event-based observations, which arise naturally in finance, seismology, and neuroscience. While there is substantial algorithmic work addressing this important problem, theoretical results are scarce. In this paper we ask the following fundamental question: what is the minimum time that one must observe the dynamics in order to exactly recover the underlying network, as a function of the number dd of interacting entities? For a class of stationary Hawkes processes with sparse, weak interactions, we prove that an observation time of order log⁡d\log d is sufficient and necessary. For the upper bound we construct a two-stage estimator that uses clipped and binned event data for screening, followed by a least-squares refinement, and apply concentration bounds derived from the Poisson cluster representation. For the lower bound we combine Fano's inequality with Jacod's Girsanov formula for point processes on a suitable subclass of networks.

Jonas Linkerhägner, Michele Bortolasi, Lorenzo Baldassari +2

University of Basel · Rice University

Temporal Point ProcessesSample ComplexityHawkes Processes
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Apr 19, 2026

FASE : A Fairness-Aware Spatiotemporal Event Graph Framework for Predictive Policing

Predictive policing systems that allocate patrol resources based solely on predicted crime risk can unintentionally amplify racial disparities through feedback driven data bias. We present FASE, a Fairness Aware Spatiotemporal Event Graph framework, which integrates spatiotemporal crime prediction with fairness constrained patrol allocation and a closed loop deployment feedback simulator. We model Baltimore as a graph of 25 ZIP Code Tabulation Areas and use 139,982 Part 1 crime incidents from 2017 to 2019 at hourly resolution, producing a sparse feature tensor. The prediction module combines a spatiotemporal graph neural network with a multivariate Hawkes process to capture spatial dependencies and self exciting temporal dynamics. Outputs are modeled using a Zero Inflated Negative Binomial distribution, suitable for overdispersed and zero heavy crime counts. The model achieves a validation loss of 0.4800 and a test loss of 0.4857. Patrol allocation is formulated as a fairness constrained linear optimization problem that maximizes risk weighted coverage while enforcing a Demographic Impact Ratio constraint with deviation bounded by 0.05. Across six simulated deployment cycles, fairness remains within 0.9928 to 1.0262, and coverage ranges from 0.876 to 0.936. However, a persistent detection rate gap of approximately 3.5 percentage points remains between minority and non minority areas. This result shows that allocation level fairness constraints alone do not eliminate feedback induced bias in retraining data, highlighting the need for fairness interventions across the full pipeline.

Pronob Kumar Barman, Pronoy Kumar Barman, Plaban Kumar Barman +1

Department of Information Systems University of Maryland, Baltimore County Baltimore, MD, USA · Department of Statistics Jagannath University Dhaka, Bangladesh · MBBS Shaheed M. Monsur Ali Medical College Sirajganj, Bangladesh

Algorithmic BiasGroup FairnessSpatiotemporal ForecastingHawkes Processes
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Apr 1, 2026

Massively Parallel Exact Inference for Hawkes Processes

Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as O(N2)O(N^2) in the number of events. The canonical linear exponential Hawkes process admits a faster O(N)O(N) recurrence, but prior work evaluates this recurrence sequentially, without exploiting parallelization on modern GPUs. We show that the Hawkes process intensity can be expressed as a product of sparse transition matrices admitting a linear-time associative multiply, enabling computation via a parallel prefix scan. This yields a massively parallelizable algorithm for estimation of linear exponential Hawkes processes. Our method reduces the computational complexity to approximately O(N/P)O(N/P) with PP parallel processors, and naturally yields a batching scheme to maintain constant memory usage, avoiding GPU memory constraints. Importantly, it computes the exact likelihood without any additional assumptions or approximations, preserving the simplicity and interpretability of the model. We demonstrate orders-of-magnitude speedups on simulated and real datasets, scaling to thousands of nodes and tens of millions of events, substantially beyond scales reported in prior work. We provide an open-source PyTorch library implementing our optimizations.

Ahmer Raza, Hudson Smith

Clemson University

Hawkes ProcessesTemporal Point ProcessesGPU Acceleration
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Mar 20, 2026

Can LLM Agents Simulate Dynamic Networks? A Case Study on Email Networks with Phishing Synthesis

While Large Language Model (LLM) multi-agent systems (MAS) offer a transformative approach to simulating human behavior in complex systems, it remains largely unexplored whether these simulations can replicate realistic structural and temporal dynamics from a dynamic network perspective. Our evaluation indicates that existing frameworks excel at generating plausible micro-level interactions but fail to capture the emergent, macroscopic topologies necessary for domains that rely on realistic network dynamics, such as modeling information propagation and cybersecurity threats. To bridge this gap, we introduce two easily integrable extensions to simulation frameworks to ensure they preserve macroscopic network fidelity: 1) augmenting LLM agents with data-driven event triggers to organically sustain long-horizon interactions, and 2) integrating Hawkes processes to accurately model temporal activation dynamics. Our approach allows LLM MAS to capture both plausible micro-level patterns and macroscopic topologies. We further demonstrate the utility of this framework in synthesizing realistic phishing campaigns within evolving communication networks. The study reveals how threats exploit structural vulnerabilities, highlighting the potential of our framework for developing next-generation defenses. Our code is available at https://github.com/Graph-COM/NSL.

Siqi Miao, Ziyang Chen, Yuhong Luo +4

Georgia Institute of Technology · University of Maryland, College Park · Rutgers University

Hawkes ProcessesLarge Language Model-Based Social SimulationMulti-Agent LLM Systems
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Mar 12, 2026

HawkesRank: Event-Driven Centrality for Real-Time Importance Ranking

Quantifying influence in networks is important across science, economics, and public health, yet widely used centrality measures remain limited: they rely on static representations, heuristic network constructions, and purely endogenous notions of importance, while offering little semantic connection to observable activity. We introduce HawkesRank, a dynamic framework grounded in multivariate Hawkes point processes that models exogenous drivers (intrinsic contributions) and endogenous amplification (self- and cross-excitation). This yields a principled, empirically calibrated, and adaptive importance measure. Classical indices such as Katz centrality and PageRank emerge as mean-field limits of the framework, clarifying both their validity and their limitations. Unlike static averages, HawkesRank measures importance through instantaneous event intensities, enabling prediction, transparent endo-exo decomposition, and adaptability to shocks. Using both simulations and empirical analysis of emotion dynamics in online communication platforms, we show that HawkesRank closely tracks system activity and consistently outperforms static centrality metrics.

Didier Sornette, Yishan Luo, Sandro Claudio Lera

Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, China · Warwick Business School, University of Warwick, Coventry, UK

Hawkes ProcessesSocial Network AnalysisComputational Social Science
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Mar 10, 2026

Stability of AI Governance Systems: A Coupled Dynamics Model of Public Trust and Social Disruptions

AI systems are increasingly entrenched in public governance, yet scholarship lacks formal tools to determine when deviations of public trust in algorithmic institutions dissipate and when they grow into collapse. Stability refers here to asymptotic recovery from finite state perturbations under fixed structural parameters. We address this gap by developing a mathematical framework for institutional trust stability that couples a Friedkin-Johnsen opinion dynamics process with a Hawkes-inspired intensity process for AI controversies. Motivated by the Computers-Are-Social-Actors literature and recent studies of trust in large language models, this bidirectional coupling reveals that governance stability depends on the structural architecture of the information environment rather than absolute trust levels. We derive an exact spectral stability criterion delineating resilience from collapse, demonstrating how event self-excitation and memory persistence systematically narrow the stable parameter regime. Our structural analysis yields four counterintuitive structural implications: high-trust systems can be structurally fragile, low-trust environments can be structurally stable, dynamical stability neither measures nor guarantees algorithmic fairness or legitimacy, and network topology reshapes equilibrium heterogeneity while its effect on spectral stability is uniformly bounded in an explicit memory-dominated regime. Governance assessment should therefore pair normative evaluation of harms and fairness with structural analysis of recoverability, rather than treating either as a proxy for the other.

Jiaqi Lai, Hou Liang, Weihong Huang

Nanyang Technological University, Singapore

Hawkes ProcessesAI GovernanceTrust in AI
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Mar 4, 2026

How Predicted Links Influence Network Evolution: Disentangling Choice and Algorithmic Feedback in Dynamic Graphs

Link prediction models are increasingly used to recommend interactions in evolving networks, yet their impact on network structure is typically assessed from static snapshots. In particular, observed homophily conflates intrinsic interaction tendencies with amplification effects induced by network dynamics and algorithmic feedback. We propose a temporal framework based on multivariate Hawkes processes that disentangles these two sources and introduce an instantaneous bias measure derived from interaction intensities, capturing current reinforcement dynamics beyond cumulative metrics. We provide a theoretical characterization of the stability and convergence of the induced dynamics, and experiments show that the proposed measure reliably reflects algorithmic feedback effects across different link prediction strategies.

Mathilde Perez, Raphaël Romero, Jefrey Lijffijt +1

LTCI, Télécom Paris, Institut Polytechnique de Paris, France. · IDLab , Ghent University , Belgium.

Hawkes ProcessesSocial Network AnalysisDynamic Graph Learning
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