Related papers: Equivalent Conditions for Weak Continuity of Nonli…
When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on…
This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling…
Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann-Kaper theory allows 1) to consider new types…
The variational formulation of nonlinear filtering due to Mitter and Newton characterizes the filtering distribution as the unique minimizer of a free energy functional involving the relative entropy with respect to the prior and an…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
We study quantile trend filtering, a recently proposed method for nonparametric quantile regression with the goal of generalizing existing risk bounds known for the usual trend filtering estimators which perform mean regression. We study…
We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…
In this paper we deal with semilinear problems at resonance. We present a sufficient condition for the existence of a weak solution in terms of the asymptotic properties of nonlinearity. Our condition generalizes the classical…
We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when…
Oftentimes in practice, the observed process changes statistical properties at an unknown point in time and the duration of a change is substantially finite, in which case one says that the change is intermittent or transient. We provide an…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
We investigate characterizations of uniformly rectifiable (UR) metric spaces by so-called weak Carleson conditions for flatness coefficients which measure the extent to which Hausdorff measure on the metric space differs from Hausdorff…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
In this paper, we consider chains of infinite order on countable state spaces with prohibited transitions. We give a set of sufficient conditions on the structure of the probability kernels of the chains to have at most one stationary…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
We study an asymptotic preserving scheme for the temporal discretization of a system of parabolic semilinear SPDEs with two time scales. Owing to the averaging principle, when the time scale separation $\epsilon$ vanishes, the slow…
The paper studies the asymptotic behavior of Random Algebraic Riccati Equations (RARE) arising in Kalman filtering when the arrival of the observations is described by a Bernoulli i.i.d. process. We model the RARE as an order-preserving,…