Related papers: On interweaving relations
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from…
In this paper we try to bridge breakthroughs in quantitative sociology/econometrics pioneered during the last decades by Mac Fadden, Brock-Durlauf, Granovetter and Watts-Strogats through introducing a minimal model able to reproduce…
We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…
Renewal theorems are developed for point processes with interarrival times $W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is a H\"older…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
We introduce time-ordered multibody interactions to describe complex systems manifesting temporal as well as multibody dependencies. First, we show how the dynamics of multivariate Markov chains can be decomposed in ensembles of…
We study a class of dynamical semigroups $(\mathbb{L}^n)_{n\in\mathbb{N}}$ that emerge, by a Feynman--Kac type formalism, from a random quantum dynamical system…
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution although these are often experimentally inaccessible. Here we propose a theory for revealing…
Latent factor models are increasingly popular for modeling multi-relational knowledge graphs. By their vectorial nature, it is not only hard to interpret why this class of models works so well, but also to understand where they fail and how…
In addition to the emergent complexity of patterns that appears when many agents come in interaction, it is also useful to characterize the dynamical processes that lead to their self-organization. A set of ergodic invariants is identified…
The expansion of global production networks has raised many important questions about the interdependence among countries and how future changes in the world economy are likely to affect the countries' positioning in global value chains. We…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
Let $X:=(X_t)_{t\geq 0}$ be an ergodic Markov process on $\real^d$, and $p>0$. We derive upper bounds of the $p$-Wasserstein distance between the invariant measure and the empirical measures of the Markov process $X$. For this we assume,…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
Given a birth-death process on $\mathbb {N}$ with semigroup $(P_t)_{t\geq0}$ and a discrete gradient ${\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\partial}_uP_t=Q_t\,{\partial}_u$,…
The aim of this paper is to provide a new method for learning the relationships between data that have been obtained independently. Unlike existing methods like matching, the proposed technique does not require any contextual information,…