Related papers: Aggregation of autoregressive processes and long m…
We investigate the dynamics of an inertial active Ornstein-Uhlenbeck (OU) particle in the presence of stochastic resetting. Using renewal approach, we compute the mean square displacement (MSD) and position probability distribution…
Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological…
We explore a key architectural aspect of deep convolutional neural networks: the pattern of internal skip connections used to aggregate outputs of earlier layers for consumption by deeper layers. Such aggregation is critical to facilitate…
In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of $q_{m}$-exponencial, form…
We establish sufficient conditions for the existence, and derive explicit formulas for the $\kappa$'th moments, $\kappa \geq 1$, of Markov modulated generalized Ornstein-Uhlenbeck processes as well as their stationary distributions. In…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple…
Application of the phase modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The phase modulation of the light causes modulation of the signal. Separation of the spectral components of the…
Many relevant statistical and econometric models for the analysis of longitudinal data include a latent process to account for the unobserved heterogeneity between subjects in a dynamic fashion. Such a process may be continuous (typically…
This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this…
Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the…
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…
We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a…
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…
Operation of the array of coupled oscillators underlying the associative memory function is demonstrated for various interconnection schemes (cross-connect, star phase keying and star frequency keying) and various physical implementation of…
We address the problem to estimate a Kronecker graphical model corresponding to an autoregressive Gaussian stochastic process. The latter is completely described by the power spectral density function whose inverse has support which admits…
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised.…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…