Related papers: Random sampling of long-memory stationary processe
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Memory replay may be key to learning in biological brains, which manage to learn new tasks continually without catastrophically interfering with previous knowledge. On the other hand, artificial neural networks suffer from catastrophic…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…
Optical memory effects are well-known types of amplitude-domain wave correlation enabling control over light scattered through diffusive materials or multimode fibers. In this letter, we report the phenomenon of random polarization memory…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…
Motivated by recent experiments we consider a stochastic lineshape theory for the case when the underlying process obeys power-law statistics, based on a generalized Anderson-Kubo oscillator model. We derive an analytical expression for the…
A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is…
Late long-term potentiation (L-LTP) appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay…
In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
Extremal clusters of stationary processes with long memory can be quite intricate. For certain stationary infinitely divisible processes with subexponential tails, including both power-like tails and certain lighter tails, e.g.…
Long short-term memory recurrent neural networks (LSTM-RNNs) are considered state-of-the art in many speech processing tasks. The recurrence in the network, in principle, allows any input to be remembered for an indefinite time, a feature…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…