Related papers: Random sampling of long-memory stationary processe
We examine the asymptotic behaviour of the sample autocovariance in a continuous-time moving average model with long-range dependence. We show that it is either asymptotically Rosenblatt distributed or stable distributed. This shows that…
Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed…
Episodic memory is a psychology term which refers to the ability to recall specific events from the past. We suggest one advantage of this particular type of memory is the ability to easily assign credit to a specific state when remembered…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
A systematic investigation of the effect of the history force on particle advection is carried out for both heavy and light particles. General relations are given to identify parameter regions where the history force is expected to be…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured…
We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no…
Large Language Models (LLMs) frequently memorize long sequences verbatim, often with serious legal and privacy implications. Much prior work has studied such verbatim memorization using observational data. To complement such work, we…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is…
The paper deals with a question of robustness of inferences, carried out on a continuous-time stationary process contaminated by a small trend, to this departure from stationarity. We show that a smoothed periodogram approach to parameter…
Catastrophic forgetting affects the training of neural networks, limiting their ability to learn multiple tasks sequentially. From the perspective of the well established plasticity-stability dilemma, neural networks tend to be overly…
We study the statistical properties of random numbers under the Martin-L\"of definition of randomness, proving that random numbers obey analogues of Strong Law of Large Numbers, the Law of the Iterated Logarithm, and that they are normal.…
Newtonian, undamped motion in single-well potentials belong to a class of well-studied conservative systems. Here, we investigate and compare long-time properties of fully deterministic motions in single-well potentials with analogous…
While recurrent neural networks have found success in a variety of natural language processing applications, they are general models of sequential data. We investigate how the properties of natural language data affect an LSTM's ability to…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate…