Related papers: Loop measures without transition probabilities
We prove an apparently novel concentration of measure result for Markov tree processes. The bound we derive reduces to the known bounds for Markov processes when the tree is a chain, thus strictly generalizing the known Markov process…
A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for…
The classical isomorphism theorems for reversible Markov chains have played an important role in studying the properties of local time processes of strongly symmetric Markov processes~\cite{mr06}, bounding the cover time of a graph by a…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations…
We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
Motivated by Mather theory of minimizing measures for symplectic twist dynamics, we study conformally symplectic flows on a cotangent bundle. These dynamics are the most general dynamics for which it makes sense to look at (asymptotic)…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
We construct measures for the non-Markovianity of quantum evolution with a physically meaningful interpretation. We first provide a general setting in the framework of channel capacities and propose two families of meaningful quantitative…
Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also…
We obtain a condition for the $L^q$-convergence of martingales generated by random multiplicative cascade measures for $q>1$ without any self-similarity requirements on the cascades.
We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…
As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications,…
We review some simple techniques based on monotone mass transport that allow to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these…
This paper 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…
The detection and quantification of non-Markovianity, a.k.a. memory, in quantum systems is a central problem in the theory of open quantum systems. There memory is as a result of the interaction between the system and its environment.…
Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \ge 1$. We consider the set of $C^1$ maps $f:M\to M$ which have no absolutely continuous (with respect to Lebesgue) invariant probability…
Information geometry of Markov chains has been studied using the dually flat structure of the space of transition probabilities. Although applications of this structure have been investigated, few attempts have examined its statistical…