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In this paper, we study Markov-dependent reflected autoregressive processes, and other related models the analysis of which results in a vector-valued fixed-point functional equation of a certain type. In queueing terms, such processes…
A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed…
This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have…
We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…
A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…
A load sharing system has several components and the failure of one component can affect the lifetime of the surviving components. Since component failure does not equate to system failure for different system designs, the analysis of the…
The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is…
For the application of MPC design in on-line regulation or tracking control problems, several studies have attempted to develop an accurate model, and realize adequate uncertainty description of linear or non-linear plants of the processes.…
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to…
In this paper, an approach to estimating a nonlinear deterministic model is presented. We introduce a stochastic model with extremely small variances so that the deterministic and stochastic models are essentially indistinguishable from…
We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…
This paper presents a meta-learning based, automatic distribution system load forecasting model selection framework. The framework includes the following processes: feature extraction, candidate model labeling, offline training, and online…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
We propose a framework employing stochastic differential equations to facilitate the long-term stability analysis of power grids with intermittent wind power generations. This framework takes into account the discrete dynamics which play a…
Model-reference adaptive systems refer to a consortium of techniques that guide plants to track desired reference trajectories. Approaches based on theories like Lyapunov, sliding surfaces, and backstepping are typically employed to advise…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
In this paper an efficient model based diagnostic process is described for systems whose components possess a causal relation between their inputs and their outputs. In this diagnostic process, firstly, a set of focuses on likely broken…