Extends Killing vector fields in electrovacuum spacetimes, proving non-extendibility.
problem Extension of Killing vector fields in electrovacuum spacetimes.
method Inspired by Ionescu-Klainerman's technique for Ricci flat manifolds, extends to strong null convex domains.
result Shows non-extendibility of Hawking vector field in Kerr-Newman solutions near horizons.
We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, Rácz and Wald, which was limited to the interior of th…
The paper studies Hawkes processes under mean-field limits and criticality conditions.
problem Analyzing nearly unstable Hawkes processes in a mean-field regime.
method Extending the method by Jaisson and Rosenbaum, establishing scaling limits and propagation of chaos.
result Scaling limits of Hawkes processes are stochastic Volterra diffusions of affine type, with three distinct limiting regimes.
Analogous to 4D, new Ansatz for quaternionic Kähler spaces with a free action.
problem Describing the geometry of quaternionic Kähler spaces with a free action.
method Gibbons-Hawking-like Ansatz based on quaternionic Kähler moment map.
result Explicit equivariant completion of twistor space construction.
Using Hawking Taub-NUT metric ga on R4, where a is a positive real number and finding a 4-parameter family of Killing vector fields of (R4,ga), we construct a 5-parameter family of Einstein Randers metrics with non-constant flag curvature.
Paper proves unique solutions for mean field equation on sphere.
problem Proving uniqueness of solutions for a specific equation on a sphere.
method Analyzing the mean field equation Δu=λ(1-e^u) on S^2, proving axially symmetry for even solutions.
result Zero is the only even solution for λ=6, implying rigidity of Hawking mass.
The study examines symmetry of solutions to a mean field equation on the 2-sphere, leading to rigidity results for Hawking mass.
problem Symmetry of solutions to a specific elliptic equation on the 2-sphere.
method Analysis of the elliptic equation and conditions for constant solutions.
result The equation has only constant solutions under certain conditions, implying rigidity of Hawking mass.
The paper proves partial rigidity of Hawking mass for stable CMC spheres in specific manifolds.
problem Rigidity of Hawking mass for stable CMC spheres in asymptotic flat and hyperbolic manifolds.
method Mean-field equation and monotonicity of Hawking mass, combined with Shi's rigidity results.
result If the Hawking mass of a nearly round stable CMC surface vanishes, the surface must be a standard sphere in R^3 and the interior is flat.
Proves symmetries of extremal horizons in spacetimes.
problem Proving symmetries of extremal horizons in arbitrary dimensions.
method Analyzes Killing vector fields and near-horizon geometry.
result Enhanced isometry groups and shifted Aretakis instability.
Extends Killing vector fields to beyond compact Cauchy horizons.
problem Proves existence of Killing vector fields beyond compact Cauchy horizons.
method New unique continuation theorem for wave equations through smooth compact lightlike hypersurfaces; novel Carleman type estimate.
result Killing vector field exists on both sides of the horizon.
We develop a new approach on the (1+3) threading of spacetime (M,g) with respect to a congruence of curves defined by an arbitrary timelike vector field. The study is based on spatial tensor fields and on the Riemannian spatial connection ∇⋆, which behave as 3D geometric objects. We obtain new formul…
The paper proves a Hawking-type singularity theorem using worldvolume quantum strong energy inequalities.
problem Improving classical singularity theorems with weakened energy conditions.
method Integral Ricci curvature bounds based on worldvolume quantum strong energy inequalities.
result Past geodesic incompleteness proven in cosmological scenarios.
New scalable variational Bayes methods for Hawkes processes.
problem Computational intractability of Bayesian estimation for generalised nonlinear Hawkes processes.
method Unified variational Bayes framework, adaptive mean-field approximation, sparsity-inducing procedure.
result Adaptive mean-field variational algorithm for sigmoid Hawkes processes is scalable and robust.
New method detects structural shifts in multivariate Hawkes processes.
problem Detecting changes in multivariate Hawkes processes.
method Using Fréchet statistics on overlapping windows of causal network.
result Accurately detects and characterizes changes in causal structure.
Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they 'self-excite', meaning that each arrival increases the rate of future arrivals for som…
Hawkes processes show weak causality; likelihoods are nearly equal for forward and backward event times.
problem Testing the causality of Hawkes processes with time reversal.
method Maximum likelihood estimation and goodness-of-fit tests.
result Parameter estimation of Hawkes processes is weakly dependent on the direction of time, and significant fits may favor backward time.
A new model for predicting market order book dynamics using a buffer Hawkes process.
problem Predicting the evolution of limit order books in financial markets.
method Introducing a Markovian single point process with a buffer mechanism and self-exciting effect.
result The model accurately predicts market order book dynamics and converges to Brownian motion.
Exact asymptotic solutions found for nonlinear Hawkes processes.
problem Analytical solutions for nonlinear Hawkes processes with positive and negative feedbacks.
method Field master equation approach to classify steady-state solutions.
result Explicit power law formulas for steady-state intensity distributions Pss(λ)∝λ−1−a, with a as a function of parameters. The paper models trades in dark pools using Hawkes processes.
problem Modeling clustered trades in dark pools.
method Developed a non-Markovian Hawkes process with time-dependent baseline intensity.
result Obtained closed-form formulas for the Hawkes process.
Researchers prove a new measure for a financial volatility model.
problem Modeling financial volatility with a Hawkes process.
method Prove existence of equivalent martingale measures for a Heston-Hawkes model.
result Existence of a family of equivalent martingale measures for the model.
A toolkit for learning Hawkes processes simplifies research and education.
problem Analyzing asynchronous event sequences with self- and mutually-triggering patterns.
method Implementation of learning algorithms and analysis tools for Hawkes processes.
result Systematic compilation of state-of-the-art and classic Hawkes process algorithms.
Flexible nonlinear Hawkes processes for time-varying systems.
problem Limited expressive ability of classic Hawkes processes.
method Flexible state-switching Hawkes processes with latent variable augmentation for Bayesian inference.
result Superior performance compared to state-of-the-art competitors.
Mamba Hawkes Process improves modeling of event sequences with long-term dependencies.
problem Modeling mutual inhibition and nonlinearity in asynchronous event sequences.
method Introduces Mamba Hawkes Process using Mamba state space architecture.
result MHP outperforms existing models across various datasets.
New model for clustering dependent community Hawkes processes in temporal networks.
problem Modeling strong dependence and community structure in temporal networks.
method Dependent Community Hawkes (DCH) models combining stochastic block models and Hawkes processes.
result Spectral clustering error bound derived for DCH models.
Study uses neural networks for fast Hawkes model parameter estimation in finance.
problem Estimating parameters of Hawkes models from high-frequency financial data.
method Recurrent neural networks for parameter estimation.
result Significantly faster computational performance compared to traditional methods.
Efficient inference for nonparametric Hawkes processes using Pólya-Gamma augmentation.
problem Efficient inference for nonparametric Hawkes processes.
method Pólya-Gamma augmentation, EM algorithm, mean-field variational inference.
result The proposed algorithms can recover well the underlying prompting characteristics efficiently.
Flexible Hawkes model with Gaussian process self-effects for time-dependent data.
problem Modeling time-dependent point processes with history dependence and self-effects.
method Extended Hawkes process with Gaussian process self-effects for both excitatory and inhibitory types, using Bayesian inference and mean-field variational approximation.
result Efficient approximate Bayesian inference achieved via data augmentation and mean-field variational approach.
In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to Lorentzian spacetimes. This approach is developed in [14] for proving, under the ma…
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
Warped product space-times generalize spherical symmetry results in relativity.
problem Generalizing spherical symmetry results to warped product space-times.
method Systematic geometric constructions, including the Kodama vector field and Hawking energy, with emphasis on signature independence.
result General Birkhoff-type theorems for warped product manifolds, applicable to non-Einstein solutions in general relativity.
Methodology for estimating marked Hawkes processes with neural networks.
problem Estimating conditional intensity of marked Hawkes processes.
method Proposes two models: Shallow Neural Hawkes with marks and Neural Network for Non-Linear Hawkes with Marks.
result Validation on synthetic datasets and real-world cryptocurrency order book data.
The paper establishes a central limit theorem for estimating the influence parameter in a partially observed Hawkes process system.
problem Estimating the influence parameter in a partially observed Hawkes process system.
method Central limit theorem applied to an estimator of the influence parameter in a partially observed system of Hawkes processes.
result Establishes a central limit theorem for the estimator of the influence parameter under the subcritical condition.
Modeling price formation with interacting Hawkes processes leading to stochastic volatility with leverage.
problem Capturing the complex dynamics of price formation in financial markets.
method Agent-based approach to aggregate self-exciting point processes with mean-field interaction.
result Aggregated model converges to a stochastic volatility model with leverage effect and faster-than-linear mean reversion.
New model uses variance-Hawkes process to fit energy market returns.
problem Modeling clustering effects in financial markets.
method Defining and fitting a variance-Hawkes process to energy market returns.
result Demonstrated that variance-Hawkes process can capture clustering effects.
Study of coupled Hawkes processes with rough-volatility limits.
problem Understanding coupled Hawkes processes with rough-volatility limits.
method Proving weak convergence of rescaled intensity vector to stochastic Volterra equations.
result Limiting components exhibit different degrees of roughness and cross-decorrelation law.
It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any compact constant mean curvature hypersurface can be covered by a foliation of compact constant mean curvature hypersurfaces. Moreover, the …
We consider a general 4n-dimensional quaternionic Kahler geometry with a free action of the torus T^(n+1). The toric action lifts onto the Swann bundle of the quaternionic Kahler space to a tri-holomorphic action that commutes with the standard H* action on the bundle. By matching Pedersen and Poon's generalized Gibbon…
Study finds small surfaces in space times with new functionals.
problem Investigating small surfaces in space times without symmetry assumptions.
method Introducing Hawking type functionals and analyzing their properties.
result Characterization of concentration points and expansion of critical surfaces.
Derives a pricing formula for VIX options using a new stochastic volatility model.
problem Pricing VIX options under a new stochastic volatility model with volatility clustering.
method Derives a semi-analytical pricing formula using the Heston-Hawkes model with an independent compound Hawkes process.
result Derives an explicit expression for VIX^2 as a linear combination of variance and Hawkes intensity.
Study of spacelike singularities in spherical spacetimes with scalar matter.
problem Characterize spacelike singularities in spherically symmetric spacetimes with scalar matter.
method Analyzes the properties of spacelike singularities in spherically symmetric spacetimes with scalar matter, proving inverse polynomial blow-up rates and providing a BKL-type expansion.
result Provides a rigorous description of Kasner-like singularities in spherically symmetric gravitational collapse.
Study Hessian geometry of Gibbons-Hawking metrics and their phase changes.
problem Understanding phase changes in Gibbons-Hawking metrics.
method Analysis via moment maps of Hessian geometry.
result Characterization of phase changes in Gibbons-Hawking metrics.
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…
Proposes a method to align Hawkes processes across different event spaces.
problem Aligning Hawkes processes in multiple event spaces.
method Fused Gromov-Wasserstein alignment for Hawkes processes.
result The method effectively aligns Hawkes processes and their event types.
Study applies Hawkes volatility to mid-price process for real-time risk management.
problem Lack of studies on Hawkes volatility for tick-level price dynamics.
method Derived variance formula for unmarked and marked Hawkes models, applied to mid-price process.
result Reliable results and high predictive power of intraday Hawkes volatility.
Model captures both slow and fast time variations in financial data.
problem Analyzing high-frequency financial data with varying background rates.
method Developed a Hawkes process with a time-varying background rate using Bayesian estimation.
result Model significantly improves goodness-of-fit to financial data, especially during fluctuating background rates.
Efficiently estimates Hawkes process kernels using non-parametric Bayesian methods.
problem Estimating flexible Hawkes process kernels with uncertainty quantification.
method Cluster representation of Hawkes processes, Gibbs sampling, expectation maximization.
result Linear time complexity in both theoretical and empirical settings.
New optimal investment strategies for finance and insurance using Hawkes-based models.
problem Optimal investment strategies in finance and insurance for specific models.
method Solving Merton investment problems with Hawkes-based models.
result New optimal investment results for finance and insurance models.
Study of Hawkes processes in limit order books for price volatility analysis.
problem Understanding price volatility in limit order books.
method Construct and analyze general compound Hawkes processes.
result Established Law of Large Numbers and Functional Central Limit Theorems for specific variations.