相关论文: A note on rate-distortion functions for nonstation…

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…

It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…

We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…

Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of $\mathbb{P}^1$ as an isomonodromic tau function associated with a difference equation. As a…

We derive a simple general parametric representation of the rate-distortion function of a memoryless source, where both the rate and the distortion are given by integrals whose integrands include the minimum mean square error (MMSE) of the…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

We study a nonlinear partial differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators, we prove existence, uniqueness and a priori estimates of…

We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…

In this paper we consider a regression model that allows for time series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that the regression function changes at some unknown…

In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent…

In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical attainability results typically rely on compactness of the…

We consider the semantic rate-distortion problem motivated by task-oriented video compression. The semantic information corresponding to the task, which is not observable to the encoder, shows impacts on the observations through a joint…

This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…

This article is concerned with the mathematical analysis of the perturbation method for extended Kohn-Sham models, in which fractional occupation numbers are allowed. All our results are established in the framework of the reduced…

We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…

Variational principles for the rate distortion (RD) theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of Tsallis, for values of the nonextensivity parameter satisfying $ 0 < q < 1 $ and $…

We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock…

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…

We study the asymptotic behavior of posterior distributions. We present general posterior convergence rate theorems, which extend several results on posterior convergence rates provided by Ghosal and Van der Vaart (2000), Shen and Wasserman…

We investigate the estimation of parameters in the random coefficient autoregressive model. We consider a nonstationary RCA process and show that the innovation variance parameter cannot be estimated by the quasi-maximum likelihood method.…