Related papers: Backward Map for Filter Stability Analysis
We consider the reconstruction of the diffusion and absorption coefficients of the diffusion equation from the internal information of the solution obtained from the first step of the inverse photoacoustic tomography (PAT). In practice, the…
The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that…
The purpose of the present paper is to introduce and establish a notion of stability for the backward propagation of chaos with respect to (initial) data sets. Consider, for example, a sequence of discrete-time martingales converging to a…
We introduce and study a new model that we call the {\em matching model}. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be {\em matched}. There is a finite…
Parametric Instability (PI) is a phenomenon that results from resonant interactions between optical and acoustic modes of a laser cavity. This is problematic in gravitational wave interferometers where the high intra-cavity power and low…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or…
We analyze a numerical instability that occurs in the well-known split-step Fourier method on the background of a soliton. This instability is found to be very sensitive to small changes of the parameters of both the numerical grid and the…
We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in…
We study a random map $T$ which consists of intermittent maps $\{T_{k}\}_{k=1}^{K}$ and a position dependent probability distribution $\{p_{k,\varepsilon}(x)\}_{k=1}^{K}$. We prove existence of a unique absolutely continuous invariant…
A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…
This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. Given a HMM, by using convex optimization methods for nuclear norm minimization with copositive…
A stable filter has the property that it asymptotically `forgets' initial perturbations. As a result of this property, it is possible to construct approximations of such filters whose errors remain small in time, in other words…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…