Related papers: Stable central limit theorems for discrete-time la…

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of…

We study the limiting distribution of a volatility target index as the discretisation time step converges to zero. Two limit theorems (a strong law of large numbers and a central limit theorem) are established, and as an application, the…

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we…

This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…

This study investigates the efficacy of Conditional Restricted Boltzmann Machines (CRBMs) for modeling high-dimensional financial time series and detecting systemic risk regimes. We extend the classical application of static Restricted…

We prove annealed central limit theorems for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment. Under summable mixing assumptions on the…

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…

We prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result…

In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale $(W_t)_{t \geq 0}$ to prove convergence in probability, in mean and almost surely, of supercritical general branching processes (a.k.a.…

In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$ and the…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…

We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations. Stochastically driven flow models are…

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

We derive a new closed-form variance-adaptive confidence sequence (CS) for estimating the average conditional mean of a sequence of bounded random variables. Empirically, it yields the tightest closed-form CS we have found for tracking…

We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…

Thermal fluctuations play a central role in fluid dynamics at mesoscopic scales and must be incorporated into numerical schemes in a manner consistent with statistical mechanics. In this work, we develop a fluctuating lattice Boltzmann…

There is a growing literature on design-based methods to estimate average treatment effects for randomized controlled trials (RCTs) using the underpinnings of experiments. In this article, we build on these methods to consider design-based…

We present a general approach to establish the Central Limit Theorem with error bounds for sequential dynamical systems. The main tool we develop is the application to this setting of a projective metric on complex cones, following the…