Related papers: Loop measures without transition probabilities

We present a new construction of a Skorohod embedding, namely, given a probability measure mu with zero expectation and finite variance, we construct an integrable stopping time T adapted to a filtration F_t, such that W_t has the law mu,…

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 establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure may be arbitrary. The proof is entirely…

In this paper, we study the following model of hidden Markov chain: $Y_i=X_i+\epsilon_i$, $i=1,...,n+1$ with $(X_i)$ a real-valued stationary Markov chain and $(\epsilon_i)_{1\leq i\leq n+1}$ a noise having a known distribution and…

We extend the Carne--Varopoulos upper bound on the probability transitions of a Markov chain to a certain class of nonreversible processes by introducing the definition of a ``centering measure.'' In the case of random walks on a group, we…

This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

We study a compactification of the space of invariant probability measures for a transitive countable Markov shift. We prove that it is affine homeomorphic to the Poulsen simplex. Furthermore, we establish that, depending on a combinatorial…

We report on an optical setup generating more than one bit of randomness from one entangled bit (i.e. a maximally entangled state of two-qubits). The amount of randomness is certified through the observation of Bell non-local correlations.…

We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…

We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method…

The entropy production rate is central to the study of non-equilibrium systems. This parameter is closely connected to violation of time-reversal symmetry, energy consumption, efficiency, and other properties of interest; in short, it…

Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…

It is shown that the no-signaling condition is not needed in order to argue a linear quantum dynamics from standard quantum statics and the usual interpretation of quantum measurement outcomes as probabilistic mixtures.

We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…

Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to…

In this paper, without any priori assumption about the post-measurement state of system, we will examine how this state is restricted by assuming each of these following assumptions. First, by using this reasonable assumption that two…

This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…

We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…

We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…