Related papers: A short memory condition for infinitely divisible …
We establish a central limit theorem for partial sums of stationary linear random fields with dependent innovations, and an invariance principle for anisotropic fractional Brownian sheets. Our result is a generalization of the invariance…
We make an observation that facilitates exact likelihood-based inference for the parameters of the popular ARFIMA model without requiring stationarity by allowing the upper bound $\bar{d}$ for the memory parameter $d$ to exceed $0.5$:…
Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size,…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
We consider a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbations via an additive Gaussian noise. Our main study is the…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
A stochastic differential equation with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary…
It is well-known that discrete-time finite-state Markov Chains, which are described by one-sided conditional probabilities which describe a dependence on the past as only dependent on the present, can also be described as one-dimensional…
In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…
We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…
Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory…
This paper addresses the asymptotic analysis of sojourn functionals of spatiotemporal Gaussian random fields with long-range dependence (LRD) in time also known as long memory. Specifically, reduction theorems are derived for local…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
Partially observable environments present a considerable computational challenge in reinforcement learning due to the need to consider long histories. Learning with a finite window of observations quickly becomes intractable as the window…
In this paper, we extend a result of Kesten and Spitzer (1979). Let us consider a stationary sequence $(\xi\_k:=f(T^k(.)))\_k$ given by an invertible probability dynamical system and some centered function $f$. Let $(S\_n)\_n$ be a simple…
In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is…
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…