Related papers: A note on rate-distortion functions for nonstation…
Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
Likelihood-based estimation methods involve the normalising constant of the model distributions, expressed as a function of the parameter. However in many problems this function is not easily available, and then less efficient but more…
We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional…
We introduce a ring of noncommutative shifted symmetric functions based on an integer-indexed sequence of shift parameters. Using generating series and quasideterminants, this multiparameter approach produces deformations of the ring of…
In this paper, we propose a novel function named Rate Distortion-in-Distortion (RDD) function as an extension of the classical rate-distortion (RD) function, where the expected distortion constraint is replaced by a Gromov-type distortion.…
We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The…
This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Due…
When the Canonical Ramsey's Theorem by Erd\H{o}s and Rado is applied to regressive functions one obtains the Regressive Ramsey's Theorem by Kanamori and McAloon. Taylor proved a "canonical" version of Hindman's Theorem, analogous to the…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to…
We present a fermion model characterized by an anticommuting-parameter shift symmetry. The Hamiltonian formulation exhibits a combination of first-class and second-class constraints. We derive the well-known Dirac equation by fixing the…
We consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable $t$, the fractional order of the self-adjoint positive definite unbounded operator in a Hilbert space and a singular…
This article is in the context of gradient compression. Gradient compression is a popular technique for mitigating the communication bottleneck observed when training large machine learning models in a distributed manner using…
This paper explores the asymptotic properties of non-autonomous Lagrangian systems, assuming that the associated Tonelli Lagrangian converges to a time-periodic function. Specifically, given a continuous initial condition, we provide a…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
The functional renormalization group equation for projectable Ho\v{r}ava-Lifshitz gravity is used to derive the non-perturbative beta functions for the Newton's constant, cosmological constant and anisotropy parameter. The resulting coupled…
The Darboux method is commonly used in the coordinate variable to produce new exactly solvable (stationary) potentials in quantum mechanics. In this work we follow a variation introduced by Bagrov, Samsonov, and Shekoyan (BSS) to include…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…