Abstract The nonlinear filter associated with the discrete time signal-observation model (Xk,Yk) is known to forget its initial condition as k →∞ regardless of the observation structure when the signal possesses sufficiently strong ergodic properties. Conversely, it stands to reason that if the observations are sufficiently informative, then the nonlinear filter should forget its initial condit...

Weak mixing is an important property for group extensions because its absence is the principal obstruction to lifting a large number of stronger mixing properties. Whether or not an extension is weakly mixing can be determined by studying the sub-extension corresponding to the quotient by the commutator subgroup. Several conditions equivalent to weak mixing are given. In particular, an extensio...

A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak metrics, a new nearest-neighbor entropy estimator is constructed and has a parameter with which the estimator is optimized to reduce its bias. It is shown that est...

We consider an L-Wasserstein type distance ρ on the configuration space ΓX over a Riemannian manifold X, and we prove that ρ-Lipschitz functions are contained in a Dirichlet space associated with a measure on ΓX satisfying certain natural assumptions. These assumptions are in particular fulfilled by the classical Poisson measures and by a large class of tempered grandcanonical Gibbs measures wi...

This paper is another case study in the program of logically analyzing proofs to extract new (typically effective) information (‘proof mining’). We extract explicit uniform rates of metastability (in the sense of T. Tao) from two ineffective proofs of a classical theorem of F.E. Browder on the convergence of approximants to fixed points of nonexpansive mappings as well as from a proof of a theo...

A Bernoulli Gibbsian line ensemble $\mathfrak{L} = (L_1, \dots, L_N)$ is the law of trajectories $N-1$ independent random walkers $L_1, L_{N-1}$ with possibly initial and terminal locations that are conditioned to never cross each other or a given up-right path $L_N$ (i.e. $L_1 \geq \cdots L_N$). In this paper we investigate asymptotic behavior sequences ensembles $\mathfrak{L}^N (L^N_1, L^N_N)...

In this work, we evaluate quantum coherence using the $$l_{1}$$ -norm and convex-roof obtain several new results. First, provide some general triangle-like inequalities of coherence, with results better than existing ones. Second, for special three-dimensional states, a method calculating is presented. Lastly, offer distinct upper bounds in measure based on state itself.

Abstract. The nonlinear filter associated with the discrete time signal-observation model (Xk, Yk) is known to forget its initial condition as k → ∞ regardless of the observation structure when the signal possesses sufficiently strong ergodic properties. Conversely, it stands to reason that if the observations are sufficiently informative, then the nonlinear filter should forget its initial con...