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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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0.4%0.8%1.2%1.5% · Aug 200119922001200920172026
10 results for superdiffusive

Study shows superdiffusive behavior in geodesic flows on curved surfaces.

problem Understanding the statistical behavior of geodesic flows on curved surfaces.
method Proved nonstandard central limit theorem with superdiffusive normalisation (tlogt)1/2(t\log t)^{1/2} for geodesic flows on nonpositively curved surfaces.
result Geodesic flows exhibit superdiffusive behavior with correlations decaying at rate t1t^{-1}.

Deep learning dynamics exhibit anomalous superdiffusion initially, aiding escape from local minima.

problem Understanding the dynamics of learning in deep neural networks.
method Novel analysis of SGD dynamics and loss landscape structure.
result SGD exhibits anomalous superdiffusion initially, transitioning to subdiffusion as learning progresses.
Financial Market Dynamicscond-mat.stat-mech

Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500…

2001-08-01abs ↗pdf ↗

The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random …

2016-08-28abs ↗pdf ↗

Paper analyzes Hit-and-Run's convergence rates and applies similar methods to randomized Kaczmarz.

problem Quantifying advantages of Hit-and-Run's coordinate-free property.
method Sharp estimates via coupling methods and mixing time bounds.
result Ballistic and superdiffusive convergence rates in certain settings.

Securities markets are quintessential complex adaptive systems in which heterogeneous agents compete in an attempt to maximize returns. Species of trading agents are also subject to evolutionary pressure as entire classes of strategies become obsolete and new classes emerge. Using an agent-based model of interacting he…

2019-12-19abs ↗pdf ↗

A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.

problem Distinguishing between sequences with different correlation degrees.
method Minimum relative entropy principle applied to cluster partitions of power-law correlated sequences.
result Optimal Hurst exponents are selected for market price series, indicating non-markovianity.

Analyzed Bitcoin market index volatility changes over two distinct periods using anomalous diffusion and multifractal analysis.

problem Characterizing volatility changes in Bitcoin market index over two distinct periods.
method Analyzed high-frequency Bitcoin data from 2019 to 2022, using anomalous diffusion and multifractal analysis.
result Volatility changes from subdiffusion to weak superdiffusion over time, with multifractal and self-similar properties.

This work models financial market returns with asymmetric Tsallis distributions, improving fit over symmetric q-Gaussians.

problem Non-symmetric behavior of stock market returns over time scales.
method Linear combination of two independent normalized half q-Gaussians with different parameters.
result Asymmetric distributions provide better fits to stock market returns than symmetric q-Gaussians, especially over longer time scales.