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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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83167250333 · Jun 202019922001200920172026
48 results for stationary measures

Stationary measures on hyperbolic surfaces with cusps are singular and stable under quasi-symmetries.

problem Understanding stationary measures on hyperbolic surfaces with cusps.
method Analyzing exponential decay of cusp excursions and proving quasi-symmetry stability.
result Stationary measures on hyperbolic surfaces with cusps are quasi-symmetrically stable and singular.

Study shows singularity of stationary measure on Furstenberg boundary for certain random walks.

problem Singularity of stationary measure on Furstenberg boundary for random walks.
method Analysis of random walks on semisimple Lie groups with specific properties.
result Stationary measure is singular to Lebesgue measure in certain cases.

Study stationary measures and orbit closures for non-abelian actions on surfaces.

problem Classify stationary measures and orbit closures for non-abelian action on a surface.
method Use a finite verifiable average growth condition and results from Brown and Rodriguez Hertz.
result Show that under certain conditions, the only nonatomic stationary measure is the given smooth invariant measure, and every orbit closure is either finite or dense.

The paper examines random walks on metric spaces and finds commensurable subgroups.

problem Determining commensurable subgroups via stationary measures in metric spaces.
method Analyzing random walks on isometry groups of metric spaces with non-singular stationary measures.
result Subgroups generated by random walks are commensurable under mild conditions.

The paper studies the dimension of limit sets using variational principles and stationary measures.

problem Calculating the Hausdorff dimension of limit sets of Anosov representations and the Rauzy gasket.
method Established variational principles for affinity exponents and Rauzy gaskets, combined with dimension formulas of stationary measures.
result Yields the equality between the Hausdorff dimensions and affinity exponents in both settings.

Neural networks' weights don't converge to stationary points but training loss stabilizes.

problem The disconnect between theoretical analyses and neural network training practice.
method An invariant measure perspective inspired by ergodic theory of dynamical systems.
result The distribution of weights converges to an approximate invariant measure, explaining loss stabilization.

The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.

problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.

The paper studies limit sets on P(R3)\mathbb{P}(\mathbb{R}^3) using stationary measures.

problem Investigating the Hausdorff dimension of limit sets on P(R3)\mathbb{P}(\mathbb{R}^3) for SL3(R)\mathrm{SL}_3(\mathbb{R}).
method Using stationary measures to generalize the Patterson-Sullivan formula and establish dimension formulas.
result Sharp lower bounds and Hausdorff dimensions for Anosov representations and the Rauzy gasket.

This paper proposes non-stationary factor models for financial stress in the UK.

problem Managing financial vulnerabilities in the UK's complex financial system.
method Creation of non-stationary factor models to capture financial stress.
result Non-stationary factor models can better capture financial stress, especially tail events.

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S^2, then the singular sets of stationary map…

1999-05-01abs ↗pdf ↗

Study local minimizers of Ginzburg-Landau functionals in high dimensions, showing energy measures converge to rectifiable measures.

problem Investigating minimizers of Ginzburg-Landau functionals in high dimensions with energy bounds.
method Analyzing minimizers with logarithmic energy bounds and considering the vacuum manifold's homotopy classes.
result Normalized energy measures converge to an (n2)(n-2)-rectifiable measure associated with a stationary varifold.

The paper models financial markets using information theory to minimize information.

problem Understanding the dynamics of financial markets.
method Modeling financial market dynamics with independent stationary scalar diffusions, interpreting the market as a communication system, and minimizing information-theoretical joint information.
result Financial market dynamics are represented by squared radial Ornstein-Uhlenbeck processes with additivity and self-similarity properties.

We characterize stationary solutions to McKean-Vlasov equations on the circle.

problem Stationary solutions of McKean-Vlasov equations on the circle.
method Exact equivalence to an infinite-dimensional quadratic system of equations over Fourier coefficients, leading to explicit characterization of stationary states.
result Analytic expressions for the emergence, form, and shape of bifurcations involving multiple Fourier modes, and connections with discontinuous phase transitions.

Study on financial systems using perturbed unimodal maps with heteroscedastic noise.

problem Analyzing systemic risk in financial systems using mathematical models.
method Investigation of one-dimensional unimodal maps perturbed by heteroscedastic noise, proving stability, convergence, and Lyapunov exponent continuity.
result Continuous dependence of average Lyapunov exponent on Markov chain parameters, and Gumbel's law for extreme values.

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We i…

2013-07-20abs ↗pdf ↗

The Cannon-Thurston map's pushed measures on the circle are singular with respect to sphere measures.

problem Understanding the behavior of geodesics and measures on fibered hyperbolic 3-manifolds.
method Properties of geodesics and measures on the circle and sphere are analyzed to prove singularity.
result Natural measures on the circle become singular with respect to measures on the sphere.

Enhances time-series regression trees with latent factors for robust financial analysis.

problem Handling predictors with measurement error, trends, seasonality, and missing data.
method Integrates latent stationary factors extracted via state-space methods into time-series regression trees.
result Factor-augmented trees provide a reliable approach for macro-finance problems, exemplified by the lead-lag effect between equity volatility and the business cycle.

Flexible GP model improves wind power prediction accuracy.

problem Accurate probabilistic prediction of wind power for grid stability.
method Heteroscedastic non-stationary Gaussian process with generalised spectral mixture kernel.
result The proposed model outperforms conventional GP models in wind power prediction.

The paper studies risk-sensitive MDPs with recursive risk measures.

problem Risk-sensitive decision-making in MDPs with unbounded costs.
method Recursive application of static risk measures, Bellman equation derivation, existence of optimal policies.
result Existence of Markovian optimal policies for infinite planning horizons, contractive model for stationary optimal policy.

The paper proves an energy identity for harmonic maps near singularities.

problem Analyzing the behavior of harmonic maps near singular points.
method Analyzes sequences of stationary harmonic maps with bounded energy, proving an energy identity near singularities.
result The energy density of the defect measure is the sum of the energies of the bubbling maps.

Improved sampling from mean-field stationary distributions.

problem Sampling from the stationary distribution of mean-field SDEs.
method Decoupling the problem into two aspects: approximation of mean-field SDE and sampling from finite-particle distribution.
result Improved guarantees in various settings, including optimizing neural networks.

The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters toward stationarity. Here, we derive stationary fluctuation-dissipation relations t…

2018-09-28abs ↗pdf ↗

New findings show Bregman proximal algorithms can get stuck near non-stationary points.

problem Bregman proximal algorithms can get stuck near non-stationary points, misleadingly suggesting convergence.
method Analysis of Bregman proximal algorithms and their behavior near non-stationary points.
result Bregman proximal algorithms can get stuck near spurious stationary points, even in convex problems.

Develops a mean-field theory for multi-head self-attention under cross-entropy training.

problem Mean-field analysis of multi-head self-attention under cross-entropy training.
method Mean-field theory for a simplified single-layer causal multi-head self-attention model.
result Proves a static finite-head approximation bound for the optimal risk.

Efficient methods reduce projections in non-stationary online learning.

problem Optimizing dynamic and adaptive regret in non-stationary online learning environments.
method Presented efficient methods reducing the number of projections per round from O(logT)O(\log T) to 11.
result Reduced number of projections per round from O(logT)O(\log T) to 11 for optimizing dynamic and adaptive regret.

New algorithm reduces dynamic regret for MDPs with unknown transition and adversarial rewards.

problem Episodic linear mixture MDPs with unknown transition and adversarial rewards.
method Combines occupancy-measure-based global optimization and policy-based variance-aware value-targeted regression.
result Achieves near-optimal dynamic regret of O~(dH3K+HK(H+PˉK))\widetilde{\mathcal{O}}(d \sqrt{H^3 K} + \sqrt{HK(H + \bar{P}_K)}).

Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.

problem Optimizing decision-making under risk in Markov processes.
method Analyzes risk-sensitive criteria using Optimized Certainty Equivalent, including entropic risk and Conditional Value-at-Risk.
result Conditions for the existence of optimal policies and solution procedures are provided.

New algorithms adaptively calibrate predictions in non-stationary environments, matching optimal rates.

problem Designing online prediction algorithms that adapt to varying levels of non-stationarity.
method Epoch-based scheduling and non-uniform partitioning of the prediction space.
result Achieves adaptive calibration guarantees under multiple measures with optimal rates.

Study MNL-Bandit in non-stationary settings with optimal regret bound.

problem Optimizing decisions in a non-stationary environment for multi-armed bandit problems.
method Develops an algorithm with worst-case expected regret bound and introduces new techniques to handle non-stationarity.
result Optimal regret bound proven for the MNL-Bandit problem in non-stationary environments.

We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2+1)-gravity, these spacetimes correspond to models containing massive particles with spin. We analyse t…

2011-08-04abs ↗pdf ↗

New algorithms find near-stationary points in convex optimization.

problem Finding near-stationary points in convex optimization.
method Memory-saving variant of OGM-G, accelerated SVRG, adaptively regularized accelerated SVRG.
result Schemes achieve fast rates for minimizing gradient norm and function value.

Memory-based models can learn to approximate Bayes-optimal predictors for non-stationary data.

problem Learning from non-stationary data with unobserved switching points.
method Memory-based neural models, including Transformers, LSTMs, and RNNs, trained to minimize log loss.
result Memory-based models can accurately approximate known Bayes-optimal algorithms and perform Bayesian inference over latent switching points.

A new confidence measure improves self-training in biased data.

problem Improving self-training in biased data.
method Proposes a new confidence measure, T-similarity, based on ensemble diversity of linear classifiers.
result Empirically shows the benefit of T-similarity for pseudo-labeling policies on various datasets.

New model identifies regimes in non-stationary data.

problem Identifying latent regimes in non-stationary systems with instantaneous effects.
method Identifiable Markov Switching Models with exponential family noise.
result Established identifiability of latent regimes and causal structures.

Study tackles non-stationary bandit convex optimization with new algorithms.

problem Minimizing regret in non-stationary environments with various measures of non-stationarity.
method Proposed Tilted Exponentially Weighted Average with Sleeping Experts (TEWA-SE) for strongly convex losses and clipped Exploration by Optimization (cExO) for general convex losses.
result Proved minimax-optimality of TEWA-SE for strongly convex losses and introduced cExO for general convex losses.