Related papers: A Markov Chain based method for generating long-ra…
We introduce a generalization of temporal-difference (TD) learning to networks of interrelated predictions. Rather than relating a single prediction to itself at a later time, as in conventional TD methods, a TD network relates each…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These…
Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations…
We prove a sample path large deviation principle (LDP) with sub-linear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space $\mathbb{D}[0,T]$ equipped with the…
We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with a pair of states of the other and…
Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
Markovian-regime-switching (MRS) models are commonly used for modelling economic time series, including electricity prices where independent regime models are used, since they can more accurately and succinctly capture electricity price…
Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…
Let $\{X_n\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set ${\cal X}$. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times $\lambda_n$…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…
This paper criticises the notion that long-range dependence is an important contributor to the queuing behaviour of real Internet traffic. The idea is questioned in two different ways. Firstly, a class of models used to simulate Internet…
This paper aims to initiate the research on dependence control, which transforms the dependence structure of a stochastic process in the system through dependence manipulation, to improve the system performance. Specifically, we develop a…
In order to capture the dependence in the upper tail of a time series, we develop non-negative regularly-varying time series models that are constructed similarly to classical non-extreme ARMA models. Rather than fully characterizing tail…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
Most of animal and human behavior occurs on time scales much longer than the response times of individual neurons. In many cases, it is plausible that these long time scales emerge from the recurrent dynamics of electrical activity in…
We present a generative model of human mobility in which trajectories arise as realizations of a prescribed, time-dependent Markov dynamics defined on a spatial interaction network. The model constructs a hierarchical routing structure with…