Related papers: A method for inferring hierarchical dynamics in st…

Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…

An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…

In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the…

The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete,…

We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…

A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…

Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents…

Modeling event dynamics is central to many disciplines. Patterns in observed event arrival times are commonly modeled using point processes. Such event arrival data often exhibits self-exciting, heterogeneous and sporadic trends, which is…

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

We cast episodic Markov decision process (MDP) planning as Bayesian inference over policies. A policy is treated as the latent variable and is assigned an unnormalized probability of optimality that is monotone in its expected return,…

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…

This work discusses a closed-loop control strategy for complex systems utilizing scarce and streaming data. A discrete embedding space is first built using hash functions applied to the sensor measurements from which a Markov process model…

The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…

We derive new discrete event simulation algorithms for marked time point processes. The main idea is to couple a special structure, namely the associated local independence graph, as defined by Didelez arXiv:0710.5874, with the activity…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…