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The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
In practice, there are processes where the in-control mean and standard deviation of a quality characteristic is not stable. In such cases, the coefficient of variation (CV) is a more appropriate measure for assessing process stability. In…
Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
Motivated by sequential detection of transient signals in high dimensional data stream, we study the performance of EWMA, MA, CUSUM, and GLRT charts for detecting a transient signal in multivariate data streams in terms of the power of…
Experiments with pedestrians could depend strongly on initial conditions. Comparisons of the results of such experiments require to distinguish carefully between transient state and steady state. In this work, a feasible algorithm -…
Mobility management is a major challenge for the wide-spread deployment of millimeter-wave (mmWave) cellular networks. In particular, directional beamforming in mmWave devices renders high-speed mobility support very complex. This…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?)…
The Exponentially Weighted Average (EWA) of observations is known to be state-of-art estimator for tracking expectations of dynamically varying data stream distributions. However, how to devise an EWA estimator to rather track quantiles of…
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or…
Averaging, or smoothing, is a fundamental approach to obtain stable, de-noised estimates from noisy observations. In certain scenarios, observations made along trajectories of random dynamical systems are of particular interest. One popular…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
In the semiconductor manufacturing batch processes, each step is a complicated physiochemical batch process; generally it is difficult to perform measurements online or carry out the measurement for each run, and hence there will be delays…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
We extend the weighted ensemble (WE) path sampling method to perform rigorous statistical sampling for systems at steady state. The straightforward steady-state implementation of WE is directly practical for simple landscapes, but not when…
Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to…
Monitoring for changes in a predictive relationship represented by a fitted supervised learning model (i.e., concept drift detection) is a widespread problem in modern data-driven applications. A general and powerful Fisher score-based…
We present Kernel-QuantTree Exponentially Weighted Moving Average (KQT-EWMA), a non-parametric change-detection algorithm that combines the Kernel-QuantTree (KQT) histogram and the EWMA statistic to monitor multivariate data streams online.…