303 papers
This paper establishes the central limit theorem for the temporal average of the backward Euler–Maruyama method applied to stochastic ordinary differential equations with super-linearly growing drift coefficients, deriving the result through direct analysis for sub-optimal deviation orders and via a Poisson equation approach for the optimal strong order.
This paper proposes and analyzes a simultaneous M-estimator for detecting a change point and recovering diffusivity values in a stochastic heat equation with space-dependent diffusivity, demonstrating that the change point converges at rate while diffusivity constants converge at rate based on local spatial measurements.
This paper establishes the strong convergence rate of an Euler-Maruyama numerical scheme for one-dimensional stochastic differential equations with distributional drifts in Hölder-Zygmund spaces, supported by theoretical bounds and numerical implementation.
This paper establishes that homogenisation and renormalisation commute for the two-dimensional periodic generalised parabolic Anderson model by introducing a novel solution ansatz to handle variable coefficients and demonstrating that the standard model can be constructed via para-controlled calculus without commutator estimates.
This paper proposes a graph signal processing framework for reversible Markov chains that defines optimal graph filters—specifically Bernstein, Chebyshev, and Legendre filters—to significantly accelerate the convergence of ergodic averages compared to traditional methods.
This paper demonstrates that in the independent cascade model on undirected graphs with symmetric influence probabilities, the local symmetry of the network structure induces a global symmetry in activation dynamics, ensuring that the probability of node being activated within steps starting from node is identical to the reverse scenario, a result established through a novel random matrix approach.
This paper establishes the scaling limits of large uniform random trees with fixed vertex degrees and heights by analyzing root-to-vertex paths via coalescent processes, thereby deriving the scaling limits of Bienaymé-Galton-Watson trees in varying environments.
This paper introduces an optimal uniform mean estimator that, by combining Talagrand's generic chaining with single-variable mean estimation, achieves a near-optimal error bound for classes of mean-zero functions under minimal assumptions, thereby resolving key challenges in high-dimensional probability and statistics.
This paper derives identities for the exit problems and resolvents of a hybrid process that switches between two Lévy processes based on a level-dependent Poissonian barrier, expressing these results through generalized scale functions and applying them to calculate ruin probabilities in risk processes with delayed dividend payments.
This paper derives explicit total variation error bounds for approximating the number of maxima and near-maxima in independent samples using logarithmic, Poisson, and negative binomial distributions, supported by new applications of Stein's method and illustrated through geometric, Gumbel, and uniform examples.
This paper establishes a standard Central Limit Theorem for the normalized number of triangles in a modified edge-triangle Exponential Random Graph model, valid across the entire analyticity region of the free energy and derived via a polynomial representation of the partition function.
This paper investigates Benford's law in stick and box fragmentation models by reducing multi-proportion stick fragmentation to a single-proportion case using combinatorial identities, establishing necessary and sufficient conditions for strong Benford convergence based on irrationality exponents, and proving that high-dimensional box fragmentation satisfies strong Benford behavior under mild conditions.
This paper introduces a novel approach using disintegration maps to establish criteria for identifying metric measure foliations based on the geometric arrangement of conditional measure supports in Wasserstein space, while also demonstrating the framework's application to studying perturbations of such foliations.
This paper establishes explicit upper bounds on the quadratic Wasserstein distance between trained single-layer neural networks and their Gaussian process limits, demonstrating that the approximation error decays polynomially with network width while accounting for the influence of architectural parameters and training dynamics.
This paper constructs probabilistically strong, strictly dissipative solutions to the three-dimensional Euler equations with additive noise that satisfy the local energy inequality, and uses these results to establish non-unique ergodicity for the forced system.
This paper introduces a novel numerical method that combines a functional equation for the Laplace-Stieltjes transform with a moment-matching technique to efficiently and stably compute the density of the Kesten-Stigum limit for supercritical Galton-Watson processes with arbitrary offspring laws.
This paper establishes quantitative pathwise entropy bounds for a stochastic 2D vortex model on the whole space under moderate interactions by combining Donsker-Varadhan inequalities with localization techniques, and subsequently derives new energy estimates for the convergence of particle systems to the limiting process.
This paper applies a probabilistic machine learning framework to analyze Collatz stopping times up to $10^7$, demonstrating that a Bayesian hierarchical Negative Binomial regression outperforms a mechanistic odd-block generator in predictive likelihood while revealing that low-order modular structure significantly drives the observed heterogeneity.
This paper resolves a long-standing open problem by establishing a universal central limit theorem for both smooth and numerical statistics of intersection currents arising from independent Gaussian holomorphic sections in arbitrary codimensions, thereby fully extending the 2010 Shiffman–Zelditch theorem through a novel geometric framework that adapts Wiener chaos and Feynman diagram techniques to random currents on complex manifolds.
This paper characterizes fractional Malliavin-Watanabe-Sobolev spaces for all by establishing a criterion based on the integrability and fractional differentiability properties of the -transform's Bargmann-Segal norm, thereby bridging Malliavin calculus with white noise analysis and providing practical tools for analyzing objects like Donsker's delta and self-intersection local times.