Related papers: Processes with Long Memory: Regenerative Construct…
We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of…
We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our…
Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line…
This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, with a special focus on the network setting. Using contraction techniques, we study the stability of such a process and provide upper…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…
We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of…
We present the analysis of behavior of N identical finite time memories with the imperfections characterized by a step-function model, based on a study of independent copies of the geometric distribution. We show a step-by-step derivation…
We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
In this paper we present iterative methods of high efficiency by the criteria of J. F. Traub and A. M. Ostrowski. We define {\it s-nonstationary iterative processes} and prove that, for any one-point iterative process without memory, such…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
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…
We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it…
A reasonable description of the degradation process is essential for credible reliability assessment in accelerated degradation testing. Existing methods usually use Markovian stochastic processes to describe the degradation process.…
In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…
We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical…