Related papers: Measure Concentration of Hidden Markov Processes

This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…

Given a possibly discontinuous, bounded function $f:\mathbb{R}\mapsto\mathbb{R}$, we consider the set of generalized flows, obtained by assigning a probability measure on the set of Carath\'eodory solutions to the ODE ~$\dot x = f(x)$. The…

In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We…

In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…

We propose methods to estimate the individual $\beta$-mixing coefficients of a real-valued geometrically ergodic Markov process from a single sample-path $X_0,X_1, \dots,X_n$. Under standard smoothness conditions on the densities, namely,…

We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…

We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…

The fundamental limits of remote estimation of Markov processes under communication constraints are presented. The remote estimation system consists of a sensor and an estimator. The sensor observes a discrete-time Markov process, which is…

We study posterior contraction rates for mixing measures in homoscedastic location-scale mixture models with infinitely many components. While posterior convergence at the level of densities is well understood, ensuring convergence of the…

Recently two approximate Newton methods were proposed for the optimisation of Markov Decision Processes. While these methods were shown to have desirable properties, such as a guarantee that the preconditioner is negative-semidefinite when…

In this paper we study posterior consistency for different topologies on the parameters for hidden Markov models with finite state space. We first obtain weak and strong posterior consistency for the marginal density function of finitely…

In this paper we define the notion of an open Markov process. An open Markov process is a generalization of an ordinary Markov process in which populations are allowed to flow in and out of the system at certain boundary states. We show…

We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…

In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the…

The paper studies information-theoretic opacity, an information-flow privacy property, in a setting involving two agents: A planning agent who controls a stochastic system and an observer who partially observes the system states. The goal…

In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed…

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider…

The problem of missing mass in statistical inference (posed by McAllester and Ortiz, NIPS'02; most recently revisited by Changa and Thangaraj, ISIT'2019) seeks to estimate the weight of symbols that have not been sampled yet from a source.…

We propose a definition o meta-stability and obtain sufficient conditions for a sequence of Markov processes on finite state spaces to be meta-stable. In the reversible case, these conditions reduce to estimates of the capacity and the…

The problem of detecting a sinusoidal signal with randomly varying frequency has a long history. It is one of the core problems in signal processing, arising in many applications including, for example, underwater acoustic frequency line…