相关论文: Double Local-to-Unity: Inference under Nearly Nons…

In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential…

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order…

The study further explores randomized QMC (RQMC), which maintains the QMC convergence rate and facilitates computational efficiency analysis. Emphasis is laid on integrating randomly shifted lattice rules, a distinct RQMC quadrature, with…

We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…

We present a status report on a discrete approach to the the near-equilibrium statistical theory of three-dimensional turbulence, which generalizes earlier work by no longer requiring that the vorticity field be a union of discrete vortex…

We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how…

The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…

A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…

This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump-diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in…

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{\"o}dinger (NLS) equation. The method of studying the stability relies on freezing the radial…

Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…

We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…

We consider self-similar blowup for (NLS) $i\partial_t u + \Delta u + u|u|^{p-1} = 0$ in $d \ge 1$ and slightly mass-supercritical range $0 < s_c := \frac d2 - \frac{2}{p-1} \ll 1$. The existence and stability of such dynamics…

We propose a novel approach to elicit the weight of a potentially non-stationary regressor in the consistent and oracle-efficient estimation of autoregressive models using the adaptive Lasso. The enhanced weight builds on a statistic that…

Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while…

We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time series models. We show the proposed estimators are consistent and follow normal distributions in…

Empirically it has been observed that the performance of deep neural networks steadily improves as we increase model size, contradicting the classical view on overfitting and generalization. Recently, the double descent phenomena has been…

Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…

In this paper, we consider supervised learning problems such as logistic regression and study the stochastic gradient method with averaging, in the usual stochastic approximation setting where observations are used only once. We show that…