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The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…
We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
Spiking activity from populations of neurons display causal interactions and memory effects. Therefore, they are expected to show some degree of irreversibility in time. Motivated by the spike train statistics, in this paper we build a…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
We observe a length-$n$ sample generated by an unknown,stationary ergodic Markov process (\emph{model}) over a finite alphabet $\mathcal{A}$. Given any string $\bf{w}$ of symbols from $\mathcal{A}$ we want estimates of the conditional…
We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary, or locally stationary, time…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
In this paper, we examine the Renyi entropy rate of stationary ergodic processes. For a special class of stationary ergodic processes, we prove that the Renyi entropy rate always exists and can be polynomially approximated by its defining…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel…
The paper introduces a new regression model designed for situations where both the response and covariates are non-stationary extremes. This method is specifically designed for situations where both the response variable and covariates are…
The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
At the nanoscale, random effects govern not only the dynamics of a physical system but may also affect its observation. This work introduces a novel paradigm for coarse graining that eschews the assignment of a unique coarse-grained…
Reinforcement learning (RL) is an important field of research in machine learning that is increasingly being applied to complex optimization problems in physics. In parallel, concepts from physics have contributed to important advances in…