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Results for “Stochastic processes.”
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Learning to Parameterize a Stochastic Processing Using Neuromorphic Data Generation.
Abstract not provided.
Joint PCE Surrogate Construction with Uncertainty Quantification for Parameterized Stochastic Processes
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A joint PCE Surrogate Construction with Uncertainty Quantification for Parameterized Stochastic Processes Applied to Catalysis
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Construction and Performance of Polynomial Chaos Surrogates for Stochastic Processes
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Relativistic stochastic processes
Random processes in Brownian motion for solving relativistic Fokker-Planck equation
Estimation of the mean of a discrete parameter, covariance stationary, stochastic process in rotation sampling
Constrained optimization procedure for deriving linear estimator of population mean in rotation sampling
Evaluation of computing systems using functionals of a Stochastic process
An intermediate model was used to represent the probabilistic nature of a total system at a level which is higher than the base model and thus closer to the performance variable. A class of intermediate models, which are generally referred to as functionals of a Markov process, were considered. A closed form solution of performability for the case where performance is identified with the minimum value of a functional was developed.
Incompatible Stochastic Processes and Complex Probabilities
The definition of conditional probabilities is based upon the existence of a joint probability. However, a reconstruction of the joint probability from given conditional probabilities imposes certain constraints upon the latter, so that if several conditional probabilities are chosen arbitrarily, the corresponding joint probability may not exist.
The Role of Microstructure During Stochastic Processes: Void Nucleation and Abnormal Grain Growth.
Abstract not provided.
Two Problems in Applied Stochastic Processes: Scaling Limits of the Multiple Range in 1D Random Walk and Uncertainty Quantification in Satellite Imagery
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Nonequilibrium dynamics of stochastic point processes with refractoriness
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze nonstationary renewal processes.
On the stability of processes defined by stochastic difference-differential equations.
Stability of stochastic processes defined by difference differential equations, noting properties of solution, weak infinitesimal operator, etc
A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes
Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.
Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets
A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations (PDEs) for which a stochastic computational model (SCM) is available and which depend on a vector-valued random control parameter. The cost of a single numerical evaluation of this SCM is assumed to be such that only a limited number of points can be computed for constructing the training dataset (small data). Each point of the training dataset is made up of realizations from a vector-valued stochastic process (the stochastic solution) and the associated random control parameter on which it depends. The presented PLoM constrained by PDE allows for generating a large number of learned realizations of the stochastic process and its corresponding random control parameter. These learned realizations are generated so as to minimize the vector-valued random residual of the PDE in the mean-square sense. Appropriate novel methods are developed to solve this challenging problem. Three applications are presented. The first one is a simple uncertain nonlinear dynamical system with a nonstationary stochastic excitation. The second one concerns the 2D nonlinear unsteady Navier–Stokes equations for incompressible flows in which the Reynolds number is the random control parameter. Here, the last one deals with the nonlinear dynamics of a 3D elastic structure with uncertainties. The results obtained make it possible to validate the PLoM constrained by stochastic PDE but also provide further validation of the PLoM without constraint.
The analysis of a countdown as a stochastic sequential process with recycle policies
Probability density for countdown derived from stochastic process random variables
A note on the maximum sample excursions of stochastic approximation processes.
Maximum sample excursions of Kiefer-Wolfowitz stochastic approximation processes
Reducing Ground-based Astrometric Errors with Gaia and Gaussian Processes
Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2D distortion field is curl-free. Applied to several hundred 90 s exposures from the Dark Energy Survey as a test bed, we find that the GPR correction reduces the variance of the turbulent astrometric distortions ≈12× , on average, with better performance in denser regions of the Gaia catalog. The rms per-coordinate distortion in the riz bands is typically ≈7 mas before any correction and ≈2 mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas rms, the residuals to an orbit fit to riz-band observations over 5 yr of the r = 18.5 trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5D stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.