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In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given…
This article studies the effects of inter-channel time and level differences in stereophonic reproduction on perceived localization uncertainty, which is defined as how difficult it is for a listener to tell where a sound source is located.…
The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input…
This chapter reviews the fundamentals of continuous and discrete Linear Time-Invariant (LTI) systems with Single Input-Single Output (SISO). We start from the general notions of signals and systems, the signal representation problem and the…
To assess the quality of a probabilistic prediction for stochastic dynamical systems (SDSs), scoring rules assign a numerical score based on the predictive distribution and the measured state. In this paper, we propose an…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
A significantly low cost and tractable progressive learning approach is proposed and discussed for efficient spatiotemporal monitoring of a completely unknown, two dimensional correlated signal distribution in localized wireless sensor…
In this paper, we study the control properties of a new class of stochastic ensemble systems that consists of families of random variables. These random variables provide an increasingly good approximation of an unknown discrete,…
SUMMARY This work aims at quantifying the effect of inherent uncertainties from cardiac output on the sensitivity of a human compliant arterial network response based on stochastic simulations of a reduced-order pulse wave propagation…
In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not…
We develop and analyse numerical schemes for uncertainty quantification in neural field equations subject to random parametric data in the synaptic kernel, firing rate, external stimulus, and initial conditions. The schemes combine a…