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We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…
This paper addresses the problem of scheduling tasks with different criticality levels in the presence of I/O requests. In mixed-criticality scheduling, higher criticality tasks are given precedence over those of lower criticality when it…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…
In this paper, we consider consensus problems over a network of nodes, where the network is divided into a number of clusters. We are interested in the case where the communication topology within each cluster is dense as compared to the…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
Modern high-dimensional point process data, especially those from neuroscience experiments, often involve observations from multiple conditions and/or experiments. Networks of interactions corresponding to these conditions are expected to…
We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated,…
We propose a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing approaches that rely on parametric or Gaussian…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We extend Rice Formula to a process which is the sum of two independent processes: a smooth process and a pure jump process with finitely many jumps. Formulas for the mean number of both continuous and discontinuous crossings through a…
This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for…
We propose a change-point detection method for large scale multiple testing problems with data having clustered signals. Unlike the classic change-point setup, the signals can vary in size within a cluster. The clustering structure on the…
This paper tackles the problem of detecting abrupt changes in the mean of a heteroscedastic signal by model selection, without knowledge on the variations of the noise. A new family of change-point detection procedures is proposed, showing…
We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…
We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the…
Parametric sensitivity analysis is a critical component in the study of mathematical models of physical systems. Due to its simplicity, finite difference methods are used extensively for this analysis in the study of stochastically modeled…